EXAMPLE 1 Solve quadratic equations Solve the equation

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EXAMPLE 1 Solve quadratic equations Solve the equation. . a 2 x 2 =

EXAMPLE 1 Solve quadratic equations Solve the equation. . a 2 x 2 = 8 SOLUTION a. 2 x 2 = 8 x 2 = 4 x = ± 4 = ± 2 Write original equation. Divide each side by 2. Take square roots of each side. Simplify. . ANSWER The solutions are – 2 and 2

EXAMPLE 1 Solve quadratic equations b. m 2 – 18 = – 18 m

EXAMPLE 1 Solve quadratic equations b. m 2 – 18 = – 18 m 2 = 0 m= 0 ANSWER The solution is 0. Write original equation. Add 18 to each side. The square root of 0 is 0.

EXAMPLE 1 c. b 2 + 12 = 5 b 2 = – 7

EXAMPLE 1 c. b 2 + 12 = 5 b 2 = – 7 Solve quadratic equations Write original equation. 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 4 z 2 = 9.

EXAMPLE 2 Take square roots of a fraction Solve 4 z 2 = 9. SOLUTION 4 z 2 = 9 Write original equation. 9 z 2 = 4 z=± 3 2 Divide each side by 4. 9 4 Take square roots of each side. Simplify.

EXAMPLE 2 Take square roots of a fraction ANSWER The solutions are – 3

EXAMPLE 2 Take square roots of a fraction ANSWER The solutions are – 3 and 3 2 2

EXAMPLE 3 Approximate solutions of a quadratic equation Solve 3 x 2 – 11

EXAMPLE 3 Approximate solutions of a quadratic equation Solve 3 x 2 – 11 = 7. Round the solutions to the nearest hundredth. SOLUTION 3 x 2 – 11 = 7 Write original equation. 3 x 2 = 18 Add 11 to each side. x 2 = 6 Divide each side by 3. x = ± 6 Take square roots of each side.

EXAMPLE 3 Approximate solutions of a quadratic equation x ± 2. 45 Use a

EXAMPLE 3 Approximate solutions of a quadratic equation x ± 2. 45 Use a calculator. Round to the nearest hundredth. ANSWER The solutions are about – 2. 45 and about 2. 45.

EXAMPLE 1 for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve

EXAMPLE 1 for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. 1. c 2 – 25 = 0 ANSWER – 5, 5. 2. 5 w 2 + 12 = – 8 ANSWER no solution ANSWER 0 3. 2 x 2 + 11 = 11

EXAMPLE 1 for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve

EXAMPLE 1 for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. 4. 25 x 2 = 16 ANSWER – 4 5 4 , 5 5. 9 m 2 = 100 ANSWER – 10 10 3 , 3 6. 49 b 2 + 64 = 0 ANSWER no solution

EXAMPLE 1 for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve

EXAMPLE 1 for Examples 1, 2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. Round the solutions to the nearest hundredth. 7. x 2 + 4 = 14 ANSWER – 3. 16, 3. 16 8. 3 k 2 – 1 = 0 ANSWER – 0. 58, 0. 58 9. 2 p 2 – 7 = 2 ANSWER – 2. 12, 2. 12