SOLUTION: Please help me solve this equation. –9(x – 3)^2 = –7

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Question 103581This question is from textbook algebra
: Please help me solve this equation. –9(x – 3)^2 = –7 This question is from textbook algebra

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
–9(x – 3)^2 = –7
-9(x^2-6x+9)=-7 square what is in the parenthesis 1st.
-9x^2+54x-81=-7
-9x^2+54x-74=0
9x^2-54+74=0 multiply both sides times -1.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-54x%2B74+=+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=%28-54%29%5E2-4%2A9%2A74=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-%28-54%29%2Bsqrt%28+252+%29%29%2F2%5C9+=+3.8819171036882
x%5B2%5D+=+%28-%28-54%29-sqrt%28+252+%29%29%2F2%5C9+=+2.1180828963118

Quadratic expression 9x%5E2%2B-54x%2B74 can be factored:
9x%5E2%2B-54x%2B74+=+%28x-3.8819171036882%29%2A%28x-2.1180828963118%29
Again, the answer is: 3.8819171036882, 2.1180828963118. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-54%2Ax%2B74+%29