a.5 methods for solving equations failures are finger posts on the road to achievement. -c. s. lewis

A.5 Methods for A.5 Methods for Solving EquationsSolving Equations

Failures are finger posts on the road to achievement.-C. S. Lewis

DomainRecall: The domain is the set of all x values for which an expression exists.

3x 23x 3 4x 2 9x 12

Ex. Find the domain of the following expression.

Solving Rational EquationsRecall how to solve the following equation…

x2

13

5x6

Steps for Solving Rational EquationsStep 1: Factor all denominators completely.

Step 2: Determine the least common denominator.

Step 3: Multiply both sides by the LCM (distribute!).

Step 4: Solve the new polynomial equation using learned methods.

Step 5: Check for any extraneous solutions in the original equation.

Solving Rational EquationsSolve the equation.

3x 2

1x 1

7

(x 1)(x 2)

Solving Rational EquationsWhat if we have one a little more tricky?!

53x 1

2

3x 2 5x 2

Solving Quadratic Equations: GCF

x 2 2xSolve the equation. Solve the equation.

x 3 6x 2

Completing the Square (a = 1)

x 2 6x 4 0

x 2 6x 4

(x 3)2 5

x 2 6x 95

Step 1: Move c to the other side

Step 2: Add to both sides

b2

2

Step 3: Rewrite the left side as the perfect square

x b2

2

Step 4: both sides and solve!

Completing the Square (a ≠ 1)Solve the equation.

4x 2 8x 10

Equations in Quadratic Form

2x 4 9x 2 350The following equation resembles quadratic form. Let’s solve it!

Equations in Quadratic Form

(3x 4)2 6(3x 4) 160How can we solve this equation without multiplying it out?

Solving Absolute Value Equations

x 7

What does “absolute value” mean?

What is the meaning of this equation?

2x 3 7

Steps for Solving Absolute Value Equations

Step 1: Isolate absolute value on one side of the equation.

Step 2: Rewrite the equation, removing the absolute value, and plus/minus of the other side of the equation.

Step 3: Solve each equation for x.

Step 4: Check for any extraneous solutions in the original equation.

x a

x a

x a x a

Solving Absolute Value EquationsSolve the following equation for x.

3x 1 92x

A.5 Methods for A.5 Methods for Solving EquationsSolving Equations

Failures are finger posts on the road to achievement.-C. S. Lewis

Homework:Homework: