SOLUTION: x²+2x-7568=0 please explain step by step

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Question 1019537: x²+2x-7568=0 please explain step by step

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x²+2x-7568=0
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1st check for an integer solution.
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Find a pair of factors of 7568 that differ by 2:
sqrt(7568) =~ 87
7568 = 86*88
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(x-86)*(x+88) = 0
x = -88, 86
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The hard way:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-7568+=+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=%282%29%5E2-4%2A1%2A-7568=30276.

Discriminant d=30276 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+30276+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+30276+%29%29%2F2%5C1+=+86
x%5B2%5D+=+%28-%282%29-sqrt%28+30276+%29%29%2F2%5C1+=+-88

Quadratic expression 1x%5E2%2B2x%2B-7568 can be factored:
1x%5E2%2B2x%2B-7568+=+%28x-86%29%2A%28x--88%29
Again, the answer is: 86, -88. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-7568+%29