Solve ax2 bx c 0 when a 1

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EXAMPLE 3
Solve ax2 bx c 0 when a 1
Solve x2 12x 4 0 by completing the square.
x2 12x 4 0
Write original equation.
x2 12x 4
Write left side in the form x2 bx.
x2 12x 36 4 36
(x 6)2 32
Write left side as a binomial squared.
Take square roots of each side.
Solve for x.
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EXAMPLE 3
Solve ax2 bx c 0 when a 1
CHECK
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EXAMPLE 4
Solve 2x2 8x 14 0 by completing the square.
2x2 8x 14 0
Write original equation.
x2 4x 7 0
Divide each side by the coefficient of x2.
x2 4x 7
Write left side in the form x2 bx.
x2 4x 4 7 4
(x 2)2 3
Write left side as a binomial squared.
Take square roots of each side.
Solve for x.
Write in terms of the imaginary unit i.
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EXAMPLE 4
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EXAMPLE 5
Standardized Test Practice
SOLUTION
Use the formula for the area of a rectangle to
write an equation.
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EXAMPLE 5
Standardized Test Practice
3x(x 2) 72
3x2 6x 72
Distributive property
x2 2x 24
Divide each side by the coefficient of x2.
x2 2x 1 24 1
(x 1)2 25
Write left side as a binomial squared.
x 1 5
Take square roots of each side.
x 1 5
Solve for x.
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EXAMPLE 5
Standardized Test Practice
So, x 1 5 4 or x 1 5 6. You can
reject x 6 because the side lengths would be
18 and 4, and side lengths cannot be negative.
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for Examples 3, 4 and 5
GUIDED PRACTICE
Solve the equation by completing the square.
7.
3x2 12x 18 0
10.
x2 6x 4 0
8.
x2 10x 8 0
11.
6x(x 8) 12
9.
12.
4p(p 2) 100
2n2 4n 14 0