Algebra 3 Solving Quadratic Equations Worksheet - Brunel University Page 10
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13Completing the square
An arbitrary quadratic expression can be written in the form
2
2
ax
+ bx + c = a(x + B)
+ C
This form is called
completed square
and can be used for sketching the graph
or solving the corresponding quadratic equation.
Example
Complete the square on the quadratic expression
2
2x
+ 12x
23
Solution:
2
x
Step 1.
Take out the coefficient of
.
23
2
2 x
+ 6x
2
x
Step 2.
Take half the coefficient of
and add its square. To keep the expression
unchanged you should to subtract the same value
23
2
2
2
2 x
+ 6x + 3
3
2
Step 3.
Rearrange the quadratic expression in the required form
23
41
2
2
2
2 (x + 3)
9
= 2 (x + 3)
= 2(x+3)
41
2
2
Note: if a=1 you skip the first step.
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