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EXAMPLE 1

x = + – 24. x = + i 24. x = + 2 i 6. ANSWER. The solutions are 2 i 6 and –2 i 6. EXAMPLE 1. Solve a quadratic equation. Solve 2 x 2 + 11 = –37. 2 x 2 + 11 = –37. Write original equation. 2 x 2 = – 48. Subtract 11 from each side. x 2 = – 24.

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EXAMPLE 1

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  1. x = + – 24 x = +i 24 x = + 2i 6 ANSWER The solutions are 2i 6 and –2i 6 . EXAMPLE 1 Solve a quadratic equation Solve 2x2 + 11 = –37. 2x2 + 11 = –37 Write original equation. 2x2 = – 48 Subtract 11 from each side. x2 = – 24 Divide each side by 2. Take square roots of each side. Write in terms of i. Simplify radical.

  2. x = + – 13 x = +i 13 x = +i 13 ANSWER The solutions are x =i 13 and –i 13 . for Example 1 GUIDED PRACTICE Solve the equation. 1. x2 = –13. x2 = –13. Write original equation. Take square roots of each side. Write in terms of i. Simplify radical.

  3. x = + – 38 x = +i 38 x = +i 38 ANSWER The solutions are x =i 38 and –i 38 . for Example 1 GUIDED PRACTICE Solve the equation. 2. x2 = –38. x2 = –38. Write original equation. Take square roots of each side. Write in terms of i. Simplify radical.

  4. x = + –8 x = +i 8 x = + 2i 2 ANSWER The solutions are 2i 2 and –2i 2 . for Example 1 GUIDED PRACTICE Solve the equation. 3. x2 + 11= 3. x2 + 11= 3. Write original equation. x2 = – 8. Subtract 11 from each side. Take square roots of each side. Write in terms of i. Simplify radical.

  5. x = + –28 x = +i 28 x = + 2i 7 ANSWER The solutions are 2i 7 and –2i 7 . for Example 1 GUIDED PRACTICE Solve the equation. 4. x2 – 8 = –36 . x2 – 8 = –36 . Write original equation. x2 = – 28. Add 8 to each side. Take square roots of each side. Write in terms of i. Simplify radical.

  6. x = + –8 x = +i 8 x = + 2i 2 ANSWER The solutions are 2i 2 and –2i 2 . for Example 1 GUIDED PRACTICE Solve the equation. 5. 3x2 – 7 = –31 . 3x2 – 7 = –31 . Write original equation. 3x2 = –24 . Add 7 to each side. x2 = –8. Divided each side by 3 Take square roots of each side. Write in terms of i. Simplify radical.

  7. x = + –6 x = +i 6 x = +i 6 ANSWER The solutions are i 6 and –i 6 . for Example 1 GUIDED PRACTICE Solve the equation. 6. 5x2 + 33 = 3 . 5x2 + 33 = 3 . Write original equation. 5x2 = –30 . Add 7 to each side. x2 = – 6. Divided each side by 3 Take square roots of each side. Write in terms of i. Simplify radical.

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