Opener-SAME SHEET-12/6 Find each square root. Solve each equation. 5. –6x = –60 6. 7. 2x – 40 = 0 8. 5x = 3 1. 6 2. 11 3. –25 4. x = 10 x = 80 x = 20

Solving Quadratic Equations by Using Square Roots 9-7 Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

5-3 Homework Quiz Find the zeros of each function. 1. f(x)= x2 –7x Find the roots of each equation using factoring. 3. x2 – 10x + 25 = 0

5-3 Homework Quiz B 1. -4x - 12 = -x2 2. 2x2 + 7x – 15 = 0 Solve by factoring 1. -4x - 12 = -x2 2. 2x2 + 7x – 15 = 0

Objective Solve quadratic equations by using square roots.

Some quadratic equations cannot be easily solved by factoring Some quadratic equations cannot be easily solved by factoring. Square roots can be used to solve some of these quadratic equations. Recall from lesson 1-5 that every positive real number has two square roots, one positive and one negative.

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. This is indicated by ±√ Positive and negative Square roots of 9

The expression ±3 is read “plus or minus three” Reading Math

Example 1A: Using Square Roots to Solve x2 = a Solve using square roots. Check your answer. x2 = 169 x2 = –49 x2 = 121 x2 = 0

If a quadratic equation is not written in the form x2 = a, use inverse operations to isolate x2 before taking the square root of both sides.

Example 2A: Using Square Roots to Solve Quadratic Equations 1. x2 – 10 =26 2. 8x2 = 32 3. 25x2 – 1 = 0 4. x2 – 32 = 17

Check It Out! Example 2a Solve by using square roots. Check your answer. 100x2 + 49 = 0 There is no real solution.

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. In this case, the answer is an irrational number. You can approximate the solutions.

Example 3A: Approximating Solutions Solve. Round to the nearest hundredth. x2 = 15

Example 4: Application Ms. Pirzada is building a retaining wall along one of the long sides of her rectangular garden. The garden is twice as long as it is wide. It also has an area of 578 square feet. What will be the length of the retaining wall? Let x represent the width of the garden.

Lesson Quiz: Part 1 Solve using square roots. Check your answers. 1. x2 – 195 = 1 2. 4x2 – 18 = –9 3. 2x2 – 10 = –12 4. Solve 0 = –5x2 + 225. Round to the nearest hundredth. ± 14 no real solutions ± 6.71