Solve quadratic equations by completing the square.

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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 9 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. 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.
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Example 2
Complete the square to form a perfect square
trinomial.
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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