kenneyfamily
3g^2  12g =  4
which number will complete the square?
a. 12
b. 4
c. 4
d. 36



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CliffSedge
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if you factor out the 3 on the left, you'll get
\(\large 3(g^24g)=4\)
Then to complete the square, add the square of half the coefficient of g.

CliffSedge
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Then, consider what would have to be added to the right side to keep both sides equal.

kenneyfamily
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4?

kenneyfamily
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@CliffSedge

CliffSedge
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Right, adding 4 inside the parentheses on the left yields
\(\large 3(g^24g+4)=4 + ?\)

kenneyfamily
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so 4 completes the square then?

smartboy23
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47

kenneyfamily
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47?

CliffSedge
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What happens when you distribute that 3 back into those parentheses on the left?

kenneyfamily
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3g^212g+12

CliffSedge
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Right, so you actually added 12 to both sides to complete the square.
\(\large 3g^2−12g+12)=−4+12\).
See?

kenneyfamily
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oh got it thanks!