SOLUTION: 3(x+3)^2=54

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Question 499928: 3(x+3)^2=54
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The way you have written the equation the exponentiation (squaring) of (x+3) would not affect the constant multiplier 3. So, my assumption is that the equation is:
3%28%28x%2B3%29%5E2%29=54
.
Divide both sides by 3.
.
(x+3)^2 = 54/3
(x+3)^2 = 18
.
x+3 = sqrt(18)
x = sqrt(18) -3
x = 3*sqrt(2) -3
.
Or we could expand the square and use factoring or quadratic equation for the solution.
.
(x+3)^2 = 54
.
x^2 +6x +9 = 54
.
x^2 +6x -45 = 0
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-45+=+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=%286%29%5E2-4%2A1%2A-45=216.

Discriminant d=216 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+216+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+216+%29%29%2F2%5C1+=+4.34846922834953
x%5B2%5D+=+%28-%286%29-sqrt%28+216+%29%29%2F2%5C1+=+-10.3484692283495

Quadratic expression 1x%5E2%2B6x%2B-45 can be factored:
1x%5E2%2B6x%2B-45+=+1%28x-4.34846922834953%29%2A%28x--10.3484692283495%29
Again, the answer is: 4.34846922834953, -10.3484692283495. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-45+%29