Objective Solve quadratic equations by using square roots.

  Example 1A: Using Square Roots to Solve x2 = a Solve using square roots. Check your answer. x2 = 169 Solve for x by taking the square root of both sides. Use ± to show both square roots. x = ± 13 The solutions are 13 and –13. Check x2 = 169 (13)2 169 169 169  x2 = 169 (–13)2 169 169 169  Substitute 13 and –13 into the original equation.

Example 1B: Using Square Roots to Solve x2 = a Solve using square roots. x2 = –49 There is no real number whose square is negative. There is no real solution.

Substitute 11 and –11 into the original equation. Check It Out! Example 1a Solve using square roots. Check your answer. x2 = 121 Solve for x by taking the square root of both sides. Use ± to show both square roots. x = ± 11 The solutions are 11 and –11. Check x2 = 121 (11)2 121 121 121  x2 = 121 (–11)2 121 121 121  Substitute 11 and –11 into the original equation.

Check It Out! Example 1c Solve using square roots. Check your answer. x2 = –16 There is no real number whose square is negative. There is no real solution.

Example 2B: Using Square Roots to Solve Quadratic Equations Solve using square roots. 2x2 – 72 = 0 2x2 – 72 = 0 +72 +72 Add 72 to both sides. 2x2 = 72 Divide by 2 on both sides. 2 2 x2 = 36 Take the square root of both sides. Use ± to show both square roots. x = ±6

Example 2B: Using Square Roots to Solve Quadratic Equations Solve using square roots. 16x2 – 49 = 0 16x2 – 49 = 0 +49 +49 Add 49 to both sides. Divide by 16 on both sides. Take the square root of both sides. Use ± to show both square roots.

Check It Out! Example 2a Solve by using square roots. Check your answer. 100x2 - 25 = 0 100x2 - 25 = 0 +25 +25 100x2 = 25 Subtract 49 from both sides. 100x2 = 25 Divide by 100 on both sides. 100 100 x2 = 25 Square root the top and bottom 100 x = ±5 = ±1 10 2

Example 3A: Approximating Solutions Solve. Round to the nearest hundredth. x2 = 15 Take the square root of both sides. x  3.87 Evaluate on a calculator. The approximate solutions are 3.87 and –3.87.

Example 3B: Approximating Solutions Solve. Round to the nearest hundredth. –3x2 + 90 = 0 –3x2 + 90 = 0 –90 –90 Subtract 90 from both sides. Divide by – 3 on both sides. x2 = 30 Take the square root of both sides. x  5.48 Evaluate on a calculator. The approximate solutions are 5.48 and –5.48.

Check It Out! Example 3c Solve. Round to the nearest hundredth. x2 + 45 = 0 x2 + 45 = 0 Subtract 45 from both sides. – 45 – 45 x2 = –45 There is no real number whose square is negative. There is no real solution.