by completing the square part 2 · lesson 23 quadratic equations solved by completing the square...
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Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook
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Solving Quadratic Equations
by Completing the Square
Part 2
MAFS.912.AREI.2.4b
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Solving Quadratic Equations by Completing the Square. when a 1.
1. Keep the terms with variables
on the SAME
side of the equation.Any constant
side of the equation.
OPPOSITE
terms should be on the
2. On the side of the equation with the variables, FACTOR OUT "a"
from the binomial.
![Page 3: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/3.jpg)
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3. Complete the square with the
ADD, the PRODUCT of "a" and the CONSTANT that wasinside the parentheses to make
a perfect square trinomial to
OPPOSITE side of the equation.
binomial inside the parentheses.
![Page 4: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/4.jpg)
Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook
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4. Factor the perfect square trinomial. Simplify the opposite side of theequation.
5. Solve the equation, using the
SQUARE ROOT Property.
![Page 5: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/5.jpg)
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EXAMPLE 1
1. Seperate the terms with variables from the constant term.
2. On the side of the equation with the variables, FACTOR OUT "a"
from the binomial.
![Page 6: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/6.jpg)
Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook
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3. Complete the square with the
ADD, the PRODUCT of "a" and the CONSTANT that wasinside the parentheses to make
a perfect square trinomial to
OPPOSITE side of the equation.
binomial inside the parentheses.
![Page 7: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/7.jpg)
Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook
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4. Factor the perfect square trinomial. Simplify the opposite side of theequation.
5. Solve the equation, using the
SQUARE ROOT Property.
![Page 8: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/8.jpg)
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EXAMPLE 2
1. Seperate the terms with variables from the constant term.
2. On the side of the equation with the variables, FACTOR OUT "a"
from the binomial.
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3. Complete the square with the
ADD, the PRODUCT of "a" and the CONSTANT that wasinside the parentheses to make
a perfect square trinomial to
OPPOSITE side of the equation.
binomial inside the parentheses.
![Page 11: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/11.jpg)
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4. Factor the perfect square trinomial. Simplify the opposite side of theequation.
5. Solve the equation, using the
SQUARE ROOT Property.
![Page 12: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/12.jpg)
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EXAMPLE 3
1. Seperate the terms with variables from the constant term.
2. On the side of the equation with the variables, FACTOR OUT "a"
from the binomial.
![Page 14: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/14.jpg)
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3. Complete the square with the
ADD, the PRODUCT of "a" and the CONSTANT that wasinside the parentheses to make
a perfect square trinomial to
OPPOSITE side of the equation.
binomial inside the parentheses.
![Page 15: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/15.jpg)
Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook
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4. Factor the perfect square trinomial. Simplify the opposite side of theequation.
5. Solve the equation, using the
SQUARE ROOT Property.
![Page 16: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/16.jpg)
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EXAMPLE 4
1. Seperate the terms with variables from the constant term.
2. On the side of the equation with the variables, FACTOR OUT "a"
from the binomial.
![Page 18: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/18.jpg)
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3. Complete the square with the
ADD, the PRODUCT of "a" and the CONSTANT that wasinside the parentheses to make
a perfect square trinomial to
OPPOSITE side of the equation.
binomial inside the parentheses.
![Page 19: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/19.jpg)
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4. Factor the perfect square trinomial. Simplify the opposite side of theequation.
5. Solve the equation, using the
SQUARE ROOT Property.
![Page 20: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing](https://reader030.vdocuments.us/reader030/viewer/2022041116/5f29cdc3cf67d56f4e0c2ffa/html5/thumbnails/20.jpg)
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EXAMPLE 5
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EXAMPLE 6
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