SOLUTION: show me how to solve this equation 2(x-8)^ 2+x^2=x(x=51)-43x

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Question 548842: show me how to solve this equation 2(x-8)^ 2+x^2=x(x=51)-43x
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
2*(x-8)^2 +x^2 = x*(x-51) - 43*x
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Use FOIL to expand the second term.
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2*(x^2-16x+64) +x^2 = x*(x-51) - 43*x
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Use the distributive property to eliminate the parentheses.
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2x^2 -32x + 128 +x^2 = x^2 -51x - 43x
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Collect terms
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3x^2 -32x + 128 = x^2 -94x
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Subtract x^2 from both sides
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2x^2 -32x + 128 = -94x
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Add 94x to both sides
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2x^2 +62x + 128 = 0
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Divide both sides by 2
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x^2 +31x + 64 = 0
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B31x%2B64+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2831%29%5E2-4%2A1%2A64=705.

Discriminant d=705 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-31%2B-sqrt%28+705+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2831%29%2Bsqrt%28+705+%29%29%2F2%5C1+=+-2.22408195264825
x%5B2%5D+=+%28-%2831%29-sqrt%28+705+%29%29%2F2%5C1+=+-28.7759180473518

Quadratic expression 1x%5E2%2B31x%2B64 can be factored:
1x%5E2%2B31x%2B64+=+1%28x--2.22408195264825%29%2A%28x--28.7759180473518%29
Again, the answer is: -2.22408195264825, -28.7759180473518. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B31%2Ax%2B64+%29