The approximate solutions are 9.49 and –9.49.Ģ5 Check It Out! Example 3b Solve. The approximate solutions are 5.48 and – 5.48.Ģ4 Check It Out! Example 3a Solve. Check Use a graphing calculator to support your answer. –3x = 0 The approximate solutions are 5.48 and –5.48. The approximate solutions are 5.48 and –5.48.Ģ3 Example 3B Continued Solve. x2 = 30 Take the square root of both sides. The approximate solutions are 3.87 and –3.87. x2 = 15 Take the square root of both sides. In this case, the answer is an irrational number. (x – 5)2 = 16 (1 – 5) (– 4) Check (x – 5)2 = 16 (9 – 5) Ģ0 When solving quadratic equations by using square roots, you may need to find the square root of a number that is not a perfect square. x = 9 or x = 1 The solutions are 9 and 1. x – 5 = ±4 x – 5 = 4 or x – 5 = –4 Write two equations, using both the positive and negative square roots, and solve each equation. (x – 5)2 = 16 (x – 5)2 = 16 Take the square root of both sides. There is no real solution.ġ8 Check It Out! Example 2b Solve by using square roots. There is no real number whose square is negative. Use ± to show both square roots.ġ6 Example 2B Continued Solve using square roots. The solution is 0.ġ5 Example 2B: Using Square Roots to Solve Quadratic Equations x2 + 7 = 7 –7 –7 x2 + 7 = 7 x2 = 0 Subtract 7 from both sides. There is no real solution.ġ3 If necessary, use inverse operations to isolate the squared part of a quadratic equation before taking the square root of both sides.ġ4 Example 2A: Using Square Roots to Solve Quadratic Equations x2 = –16 There is no real number whose square is negative. Check x2 = 0 (0)2 0 Substitute 0 into the original equation.ġ2 Check It Out! Example 1c Solve using square roots. x2 = 0 Solve for x by taking the square root of both sides. Check x2 = 121 (11) x2 = 121 (–11) Substitute 11 and –11 into the original equation.ġ1 Substitute 0 into the original equation.Ĭheck It Out! Example 1b Solve using square roots. x2 = 121 Solve for x by taking the square root of both sides. There is no real solution.ġ0 Substitute 11 and –11 into the original equation.Ĭheck It Out! Example 1a Solve using square roots. x2 = –49 There is no real number whose square is negative. Check x2 = 169 (13) x2 = 169 (–13) Substitute 13 and –13 into the original equation.ĩ Example 1B: Using Square Roots to Solve x2 = a x2 = 169 Solve for x by taking the square root of both sides. This is indicated by ±√ Positive and negative Square roots of 9Ħ The expression ☓ is read “plus or minus three”Ĩ Example 1A: Using Square Roots to Solve x2 = a Recall from Lesson 1-5 that every positive real number has two square roots, one positive and one negative.ĥ Positive Square root of 9 Negative Square root of 9 When you take the square root of a positive number and the sign of the square root is not indicated, you must find both the positive and negative square root. Square roots can be used to solve some of these quadratic equations. Some quadratic equations cannot be easily solved by factoring. x = 10 x = 80 x = 20ģ Objective Solve quadratic equations by using square roots.Ĥ Some quadratic equations cannot be easily solved by factoring Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1Ģ Warm Up Find each square root. To determine the number of solutions of each quadratic equation, we will look at its discriminant.Presentation on theme: "Solving Quadratic Equations by Using Square Roots 9-7"- Presentation transcript:ġ Solving Quadratic Equations by Using Square Roots 9-7 \)ĭetermine the number of solutions to each quadratic equation.
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