SOLUTION: {{{(x + 3)^2 = 28}}}

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Question 143961: %28x+%2B+3%29%5E2+=+28
Found 2 solutions by nabla, Zircon:
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
(x + 3)^2 = 28
expand LEFT
x^2+6x+9=28
shift RIGHT to LEFT
x^2+6x-19=0
USE QUADRATIC FORMULA
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-19+=+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-19=112.

Discriminant d=112 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+112+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+112+%29%29%2F2%5C1+=+2.29150262212918
x%5B2%5D+=+%28-%286%29-sqrt%28+112+%29%29%2F2%5C1+=+-8.29150262212918

Quadratic expression 1x%5E2%2B6x%2B-19 can be factored:
1x%5E2%2B6x%2B-19+=+1%28x-2.29150262212918%29%2A%28x--8.29150262212918%29
Again, the answer is: 2.29150262212918, -8.29150262212918. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-19+%29


Additionally,
(x + 3)^2 = 28
x+3=+/- sqrt(28)
x=-3+/-sqrt(28)
x=-3+/- 2sqrt(7)

Answer by Zircon(1) About Me  (Show Source):