SOLUTION: Hello, Please help me solve this equation: Give the exact and approximate solutions to three decimal places. {{{y^2-16y+64=1}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello, Please help me solve this equation: Give the exact and approximate solutions to three decimal places. {{{y^2-16y+64=1}}}      Log On


   

Question 582057: Hello,
Please help me solve this equation:
Give the exact and approximate solutions to three decimal places.
y%5E2-16y%2B64=1
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Give the exact and approximate solutions to three decimal places.
y%5E2-16y%2B64=1
y%5E2-16y%2B63+=+0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-16x%2B63+=+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=%28-16%29%5E2-4%2A1%2A63=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%28-16%29-sqrt%28+4+%29%29%2F2%5C1+=+7

Quadratic expression 1x%5E2%2B-16x%2B63 can be factored:
1x%5E2%2B-16x%2B63+=+%28x-9%29%2A%28x-7%29
Again, the answer is: 9, 7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-16%2Ax%2B63+%29

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