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Solving Quadratic Equations: Factoring and Square Root Method

In this section, we explore effective methods for solving quadratic equations, particularly when factoring is not an option. The Square Root Property provides a reliable alternative for finding solutions. We will apply this property through various examples to illustrate the process. Additionally, the Pythagorean Theorem is introduced, emphasizing its relationship in right triangles. We'll calculate the hypotenuse's length using given leg lengths, presenting both exact answers and decimal approximations.

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Solving Quadratic Equations: Factoring and Square Root Method

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  1. Section 7.1 – Solving Quadratic Equations

  2. We already know how to solve quadratic equations. What if we can’t factor? Maybe we can use the Square Root Property.

  3. Square Root Property If then

  4. Square Root Property p. 557 Solve each equation using the Square Root Property.

  5. Square Root Property p. 557 Solve each equation using the Square Root Property.

  6. Square Root Property p. 557 Solve each equation using the Square Root Property.

  7. Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. c a b

  8. Pythagorean Theorem p. 558 The lengths of the legs of a right triangle are given. Find the length of the hypotenuse. Give exact answers and decimal approximations rounded to two decimal places. 25 c 7 24

  9. Pythagorean Theorem p. 558 The lengths of the legs of a right triangle are given. Find the length of the hypotenuse. Give exact answers and decimal approximations rounded to two decimal places. 17 c 8 15

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