Quadratic Equation Worksheet - Completing The Square Page 2
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2
Solving a Quadratic Equation if the Coefficient of x
Is 1
E X A M P L E 2
2
Solve x
+ 10x º 3 = 0 by completing the square.
S
OLUTION
2
x
+ 10x º 3 = 0
Write original equation.
S
H
TUDENT
ELP
2
2
x
+ 10x = 3
Write the left side in the form x
+ bx.
Study Tip
In Example 2 note that
2
1
0
2
2
2
Add }
}
x
+ 10x +
5
= 3 +
25
= 5
= 25 to each side.
you must add 25 to both
2
sides of the equation
2
(x + 5)
= 28
Write the left side as a binomial squared.
2
x
+ 10x = 3 when
completing the square.
x + 5 = ± 2 8
Take square roots of each side.
x = º5 ± 2 8
Solve for x.
x = º5 ± 2 7
Simplify.
The solutions are º5 + 2 7 and º5 º 2 7 .
CHECK
You can check the solutions by
substituting them back into the original
equation. Alternatively, you can graph
2
Zero
y = x
+ 10x º 3 and observe that the
X=-10.2915
Y=0
x-intercepts are about 0.29 ≈ º5 + 2 7
and º10.29 ≈ º5 º 2 7 .
. . . . . . . . . .
2
If the coefficient of x
in a quadratic equation is not 1, you should divide each side of
the equation by this coefficient before completing the square.
2
Solving a Quadratic Equation if the Coefficient of x
Is Not 1
E X A M P L E 3
2
Solve 3x
º 6x + 12 = 0 by completing the square.
S
OLUTION
2
3x
º 6x + 12 = 0
Write original equation.
2
2
x
º 2x + 4 = 0
Divide each side by the coefficient of x
.
2
2
x
º 2x = º4
Write the left side in the form x
+ bx.
2
º
2
2
2
Add }
}
2
x
º 2x +
(º1)
= º4 +
1
= (º1)
= 1 to each side.
2
2
(x º 1)
= º3
Write the left side as a binomial squared.
x º 1 = ± º 3
Take square roots of each side.
x = 1 ± º 3
Solve for x.
x = 1 ± i 3
Write in terms of the imaginary unit i.
The solutions are 1 + i 3 and 1 º i 3 .
Because the solutions are imaginary, you cannot check them graphically.
CHECK
However, you can check the solutions algebraically by substituting them back into
the original equation.
5.5 Completing the Square
283
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