Completing The Square Using Algebra Tiles Worksheet Page 4
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1
2
3
4Now let’s solve a quadratic equation using Completing the Square.
Steps:
+ 6x −14 = 0
Example: x
You try: x
2
2
+ 8x − 20 = 0
a) Move constant term of quadratic
+ 6x −14 +14 = 0 +14
2
x
to the other side. Write the equation
+ 6x + __ = 14 + __
2
x
+ bx + __ = −c + __ form.
in ax
2
b) Complete the square by adding a
+ 6x + 9 = 14 + 9
2
x
constant to both sides.
c) Rewrite the left side of the
(x + 3)
= 25
2
equation as a binomial squared and
simplify the right side.
x + 3 = ±5
d) Square root both sides.
x + 3 = −5
x + 3 = 5
e) Solve for x.
x + 3 − 3 = −5 − 3
x + 3 − 3 = 5 − 3
x = −8
x = 2
Solve the following equations by completing the square using the steps above.
− 4x − 32 = 0
+ 8x + 7 = 0
15. x
2
16. x
2
a)
a)
b)
b)
c)
c)
d)
d)
e)
e)
If the leading coefficient ≠ 1 , we must first divide each term by “a” so that the coefficient of the x
2
term is 1.
Then complete the same steps above.
+18x +12 = 0
2
18. 3x
2
17.
2x
+ 4x − 3 = 0
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