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Quadratic Equation Solutions and Perfect Square Trinomials

Learn how to solve quadratic equations by finding square roots and how to make perfect square trinomials. Practice problems included.

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Quadratic Equation Solutions and Perfect Square Trinomials

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  1. ANSWER The solutions are 4 + 5 = 9 and 4 –5 = – 1. EXAMPLE 1 Solve a quadratic equation by finding square roots Solve x2 – 8x + 16 = 25. x2 – 8x + 16 = 25 Write original equation. (x – 4)2 = 25 Write left side as a binomial squared. x – 4 = +5 Take square roots of each side. x = 4 + 5 Solve for x.

  2. 16 = 8 2 EXAMPLE 2 Make a perfect square trinomial Find the value of cthat makes x2 + 16x + ca perfect square trinomial. Then write the expression as the square of a binomial. SOLUTION STEP 1 Find half the coefficient of x. STEP 2 Square the result of Step 1. 82 = 64 STEP 3 Replace cwith the result of Step 2. x2 + 16x + 64

  3. EXAMPLE 2 Make a perfect square trinomial ANSWER The trinomialx2 + 16x + c is a perfect square whenc = 64. Thenx2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)2.

  4. for Examples 1 and 2 GUIDED PRACTICE Solve the equation by finding square roots. 1. x2 + 6x + 9 = 36. ANSWER 3 and –9. 2. x2 – 10x + 25 = 1. ANSWER 4 and 6. 3. x2 – 24x + 144 = 100. ANSWER 2 and 22.

  5. 81 9 4 2 for Examples 1 and 2 GUIDED PRACTICE Find the value of c that makes the expression a perfect square trinomial.Then write the expression as the square of a binomial. x2 + 14x + c 4. ANSWER 49 ; (x + 7)2 x2 + 22x + c 5. ANSWER 121 ; (x + 11)2 x2 – 9x + c 6. ANSWER ; (x – )2.

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