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Published byHugh Floyd Modified over 9 years ago
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Objective Solve quadratic equations by completing the square.
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In the previous lesson, you solved quadratic equations by isolating x2 and then using square roots. This method works if the quadratic equation, when written in standard form, is a perfect square. When a trinomial is a perfect square, there is a relationship between the coefficient of the x-term and the constant term. X2 + 6x x2 – 8x + 16 Divide the coefficient of the x-term by 2, then square the result to get the constant term.
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An expression in the form x2 + bx is not a perfect square
An expression in the form x2 + bx is not a perfect square. However, you can use the relationship shown above to add a term to x2 + bx to form a trinomial that is a perfect square. This is called completing the square.
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Example 1: Completing the Square
Complete the square to form a perfect square trinomial. A. x2 + 2x + B. x2 – 6x +
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Example 2 Complete the square to form a perfect square trinomial. a. x2 + 12x + b. x2 – 5x +
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To solve a quadratic equation in the form x2 + bx = c, first complete the square of x2 + bx. Then you can solve using square roots.
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Solving a Quadratic Equation by Completing the Square
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Example 3 Solve by completing the square. Check your answer. x2 + 16x = –15
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Example 4 Solve by completing the square. Check your answer. x2 + 10x = –9
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Practice Complete the square to form a perfect square trinomial. 1. x2 +11x + 2. x2 – 18x + Solve by completing the square. 3. x2 + 6x = 144 4. x2 + 8x = 23
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