EXAMPLE 1 Solve quadratic equations

Solve the equation.

a. 2x2 = 8

SOLUTION

a. 2x2 = 8 Write original equation.

x2 = 4 Divide each side by 2.

x = ± 4 = ± 2 Take square roots of each side. Simplify.

ANSWER The solutions are –2 and 2.

Solve quadratic equationsEXAMPLE 1

b. m2 – 18 = – 18 Write original equation.

m2 = 0 Add 18 to each side.

The square root of 0 is 0.m = 0

ANSWER

The solution is 0.

Solve quadratic equationsEXAMPLE 1

c. b2 + 12 = 5 Write original equation.

b2 = – 7 Subtract 12 from each side.

ANSWER

Negative real numbers do not have real square roots. So, there is no solution.

EXAMPLE 2 Take square roots of a fraction

Solve 4z2 = 9.

SOLUTION

4z2 = 9 Write original equation.

z2 = 94 Divide each side by 4.

Take square roots of each side.z = ± 94

z = ± 32

Simplify.

Take square roots of a fractionEXAMPLE 2

ANSWER

The solutions are – and 32

32

Approximate solutions of a quadratic equation

EXAMPLE 3

Solve 3x2 – 11 = 7. Round the solutions to the nearesthundredth.

SOLUTION

3x2 – 11 = 7 Write original equation.

3x2 = 18 Add 11 to each side.

x2 = 6 Divide each side by 3.

x = ± 6 Take square roots of each side.

Approximate solutions of a quadratic equation

EXAMPLE 3

x ± 2.45 Use a calculator. Round to the nearesthundredth.

ANSWER

The solutions are about – 2.45 and about 2.45.

EXAMPLE 1 Solve quadratic equations

Solve the equation.

1. c2 – 25 = 0

GUIDED PRACTICE for Examples 1,2 and 3

ANSWER –5, 5.

2. 5w2 + 12 = – 8 ANSWER no solution

3. 2x2 + 11 = 11 ANSWER 0

EXAMPLE 1 Solve quadratic equations

Solve the equation.

4. 25x2 = 16

GUIDED PRACTICE for Examples 1,2 and 3

ANSWER 4 5

4 5– ,

5. 9m2 = 100 ANSWER 103– ,

103

6. 49b2 + 64 = 0 ANSWER no solution

EXAMPLE 1 Solve quadratic equations

Solve the equation. Round the solutions to the nearest hundredth.

7. x2 + 4 = 14

GUIDED PRACTICE

ANSWER – 3.16, 3.16

for Examples 1,2 and 3

8. 3k2 – 1 = 0 ANSWER – 0.58, 0.58

9. 2p2 – 7 = 2 ANSWER – 2.12, 2.12