SOLUTION: Solve. -9(x-3)^2=-7

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Question 92226: Solve.
-9(x-3)^2=-7
Answer by rossiv53(27) About Me  (Show Source):
You can put this solution on YOUR website!
-9%28x-3%29%5E2=-7
First, work with the exponent
-9%28x%5E2-6x%2B9%29=-7
Distribute the 9
-9%2Ax%5E2%2B54%2Ax-81=-7
Subtract 7 from both sides
-9%2Ax%5E2%2B54%2Ax-74=0
Now you can use quadratic formula to finish solving
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -9x%5E2%2B54x%2B-74+=+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=%2854%29%5E2-4%2A-9%2A-74=252.

Discriminant d=252 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-54%2B-sqrt%28+252+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2854%29%2Bsqrt%28+252+%29%29%2F2%5C-9+=+2.1180828963118
x%5B2%5D+=+%28-%2854%29-sqrt%28+252+%29%29%2F2%5C-9+=+3.8819171036882

Quadratic expression -9x%5E2%2B54x%2B-74 can be factored:
-9x%5E2%2B54x%2B-74+=+-9%28x-2.1180828963118%29%2A%28x-3.8819171036882%29
Again, the answer is: 2.1180828963118, 3.8819171036882. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-9%2Ax%5E2%2B54%2Ax%2B-74+%29

Good luck!