SOLUTION: Which of the following are solutions to the quadratic equation? Check all that apply x(exponent)2 + 12x + 36 = 7 -6 √7-6 √7 -6 -√7-6 √7+6

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Question 144747: Which of the following are solutions to the quadratic equation? Check all that apply
x(exponent)2 + 12x + 36 = 7
-6
√7-6
√7
-6
-√7-6
√7+6
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+12x+%2B+36+=+7
x%5E2+%2B+12x+%2B+29+=+0 Make it equal to zero, always.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B29+=+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=%2812%29%5E2-4%2A1%2A29=28.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+28+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+28+%29%29%2F2%5C1+=+-3.35424868893541
x%5B2%5D+=+%28-%2812%29-sqrt%28+28+%29%29%2F2%5C1+=+-8.64575131106459

Quadratic expression 1x%5E2%2B12x%2B29 can be factored:
1x%5E2%2B12x%2B29+=+%28x--3.35424868893541%29%2A%28x--8.64575131106459%29
Again, the answer is: -3.35424868893541, -8.64575131106459. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B29+%29

It's -6+sqrt%287%29, and
It's -6-sqrt%287%29