SOLUTION: HOW DO YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE

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Question 589117: HOW DO YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll pick a random quadratic:
+2x%5E2+-+9x+%2B+24+
Set equal to zero to find roots
+2x%5E2+-+9x+%2B+24+=+0+
Get the constant term on the right side
by subtracting +24+ from both sides
+2x%5E2+-+9x+=+-24+
Divide both sides by +2+
+x%5E2+-+%289%2F2%29%2Ax+=+-12+
Now take 1/2 of the coefficient of x,
divide it by 2, square it, and add it
to both sides
+x%5E2+-+%289%2F2%29%2Ax+%2B+%289%2F4%29%5E2+=+-12+%2B+%289%2F4%29%5E2+
The left side will automatically become a perfect square
+%28+x+-+9%2F4+%29%5E2+=+-%28192%2F16%29+%2B+81%2F16+
+%28+x+-+9%2F4+%29%5E2+=+-%28+111%2F16+%29+
Now take the square root of both sides
+x+-+9%2F4+=+sqrt%28+1%2F16+%29%2Asqrt%28+-111%29+
+x-+9%2F4+=+%281%2F4%29%2A10.536i+
+x+=+%281%2F4%29%2A%28+9+%2B+10.536i+%29+
and also, using the (-) square root,
+x+=+%281%2F4%29%2A%28+9+-+10.536i+%29+