SOLUTION: Solve y2 = 15y − 56 using the quadratic formula

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Question 522808: Solve y2 = 15y − 56 using the quadratic formula

Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
y^2=15y-56
y^2-15y+56=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B-15y%2B56+=+0) has the following solutons:

y%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=%28-15%29%5E2-4%2A1%2A56=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--15%2B-sqrt%28+1+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+8
y%5B2%5D+=+%28-%28-15%29-sqrt%28+1+%29%29%2F2%5C1+=+7

Quadratic expression 1y%5E2%2B-15y%2B56 can be factored:
1y%5E2%2B-15y%2B56+=+1%28y-8%29%2A%28y-7%29
Again, the answer is: 8, 7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-15%2Ax%2B56+%29