Warm Up Solve.52

54

3x52

1039

x

56

3x52

22

56

3x52

2536

3x52

2539

x52

25

25

54

54

3 2575

1

5

10-3B Radical Equations

Algebra 1 Glencoe McGraw-Hill Linda Stamper

CAUTIONCAUTION:: Squaring both sides of an equation can introduce a solution to the squared equation that does not satisfy the original equation. Such a solution is called an extraneous solution. When you solve by squaring both sides of an equation, check the solution in the original equation.Solve

.Write problem. 09x

Square each side of the equation.

Solve.

9x

22 9x

81x

Isolate the radical.

Check your solution in the original equation. 09x

0981

099 018

No solution

Solve.

Write problem.

x3x2

Simplify.

Write the quadratic equation in standard form (move to the side that will make the leading coefficient positive).

22 x3x2 2x3x2 3x2x0 2

Square each side of the equation.

Check both your solutions in the original equation.

Solve.

1x3x0 01x 03x

1x 3x

1312

Solve.

Write problem.

x3x2

Simplify.

Write the quadratic equation in standard form (move to the side that will make the leading coefficient positive).

22 x3x2 2x3x2 3x2x0 2

Square each side of the equation.

Check both your solutions in the original equation.

Solve.

1x3x0 01x 03x

1x 3x

x3x2 3332

336 39 33

x3x2

132 11 11

01x3x 01x3x

03x2x2

Solve.

Write problem.

x3x2

Simplify.

What happens when you make the leading coefficient negative?

22 x3x2 2x3x2 Square each side of the

equation.

Remember to use the X-Factor method when the leading coefficient is not a 1.

-3

2 3 –1

Wrong factors! 01x3x1 X

Remember to discard any GCF factored out after the X figure!

Solve.

x3x4 Example 1Example 2Example 3

x2x

x5x28x4

Check both your solutions in the original equation.

Example 1 Solve.

x3x4 22

x3x4 2x3x4 3x4x0 2

1x3x0 01x 03x

1x 3x

x3x4 3334

3312 39 33

x3x4 1314

134 1111

121

Check both your solutions in the original equation.

Example 2 Solve.

x2x

22 x2x 2x2x 2xx0 2

1x2x0 01x 02x 1x 2x Important points:

When the radical is isolated is it equal to a

negative?

Does the value produce a negative radicand?

x2x 222

24 22

x2x

11 11

Check both your solutions in the original equation.

Example 3 Solve.

x28x 22 x28x

x28x2 08x2x2

02x4x 02x 04x

2x 4x

4542844

42 22

x5x28x4 x5x28x4

2522824 x5x28x4

10488

x5x5

20016 2016

x6x2 )4 2

222 x6x2

22 x6x2

06x2 6x2

6x2

6x

Only positive 6

Solve.

2x2x

2x 7x

Solve.

15x162x )5

22 15x162x

15x16x4 2 015x16x4 2

03x25x2

60

-16 -10 –6

03x2 05x2

25

x

06x410x4 03x225x22

23

x

4x2x )6

2x7x0

02x 07x

224x2x

16x8x2x 2 x 2 x 2

14x9x0 2

14

-9 -7 –2

Solve.

4x8x2

x27x5 )8 2

No Solution

22 4x8x2

4x8x4 2

04x8x4 2

01x2x4 2

01x 04 2

222 x27x5

22 x47x5 07x2 7x2

7x2

7x

1x Only positive 7

01x

x24x8x4 )7 x2x2

Solve.

5x24x )9

22 5x24x

5x2x61 2 05x2x61 2

01x25x8

-80

-2 -10 8

01x2 05x8

85

x

08x1610x16 01x285x82

21

x

10-A11 Practice Workbook Page 65 #1-22.

Solve.

3x2x )1 8x6x )2

22 3x2x

3x2x2

03x2x2 01x3x

01x 03x 1x 3x

22 8x6x 8x6x2

08x6x2

02x4x

02x 04x

2x 4x

Solve.

2x3x )3 14x9x )4

22 2x3x

2x3x2

02x3x2 01x2x

01x 02x 1x 2x

No Solution

22 14x9x

14x9x2

014x9x2 02x7x

02x 07x 2x 7x