SOLUTION: Complete the square showing the steps: y=4x^2+24x-13 Thanks so much :)

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Question 1032924: Complete the square showing the steps:
y=4x^2+24x-13
Thanks so much :)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+4x%5E2+%2B+24x+-+13+
Set ++y+=+0+ to find roots
+0+=+4x%5E2+%2B+24x+-+13+
Add +13+ to both sides
+4x%5E2+%2B+24x+=+13+
Divide both sides by +4+
+x%5E2+%2B+6x+=+13%2F4+
Take 1/2 of the coefficient of +x+,
square it and add it to both sides
+x%5E2+%2B+6x+%2B+%286%2F2%29%5E2+=+13%2F4+%2B+%286%2F2%29%5E2+
Simplify
+x%5E2+%2B+6x+%2B+9+=+13%2F4+%2B+36%2F4+
+x%5E2+%2B+6x+%2B+9+=+49%2F4+
+%28+x+%2B+3+%29%5E2+=+%287%2F2%29%5E2+
Take the ( positive ) square root of both sides
+x+%2B+3+=+7%2F2+
+x+=+7%2F2+-+6%2F2+
+x+=+1%2F2+
Take the ( negative ) square root of both sides
+x+%2B+3+=+-7%2F2+
+x+=+-6%2F2+-+7%2F2+
+x+=+-13%2F2+
------------------------
check answers:
+y+=+4x%5E2+%2B+24x+-+13+
+0+=+4%2A%281%2F2%29%5E2+%2B+24%2A%281%2F2%29+-+13+
+0+=+4%2A%281%2F4%29+%2B+12+-+13+
+0+=+1+%2B+12+-+13+
+0+=+13+-+13+
+0+=+0++
and
+y+=+4x%5E2+%2B+24x+-+13+
+0+=+4%2A%28-13%2F2%29%5E2+%2B+24%2A%28-13%2F2%29+-+13+
+0+=+4%2A%28+169%2F4+%29+-+312%2F2+-+13+
+0+=+169+-+156+-+13+
+0+=+169+-+169+
+0+=+0+
OK