SOLUTION: Use the quadratic formula to solve the euation. If the equation has no real number solutions, so state. x^2 + 7x - 60 = 0

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Question 247378: Use the quadratic formula to solve the euation. If the equation has no real number solutions, so state.
x^2 + 7x - 60 = 0
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B7x-60=0
Can be factored...
%28x-5%29%28x%2B12%29=0
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So the roots are x = 5 and x = -12.
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Or by using the quadratic.
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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%2B7x%2B-60+=+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=%287%29%5E2-4%2A1%2A-60=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+289+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%287%29-sqrt%28+289+%29%29%2F2%5C1+=+-12

Quadratic expression 1x%5E2%2B7x%2B-60 can be factored:
1x%5E2%2B7x%2B-60+=+1%28x-5%29%2A%28x--12%29
Again, the answer is: 5, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-60+%29

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