SOLUTION: Use the quadratic formula to solve the following equations x^2 + 16x + 53 = 0

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Question 101017: Use the quadratic formula to solve the following equations
x^2 + 16x + 53 = 0
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B16x%2B53+=+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=%2816%29%5E2-4%2A1%2A53=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+44+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+-4.6833752096446
x%5B2%5D+=+%28-%2816%29-sqrt%28+44+%29%29%2F2%5C1+=+-11.3166247903554

Quadratic expression 1x%5E2%2B16x%2B53 can be factored:
1x%5E2%2B16x%2B53+=+%28x--4.6833752096446%29%2A%28x--11.3166247903554%29
Again, the answer is: -4.6833752096446, -11.3166247903554. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B16%2Ax%2B53+%29