SOLUTION: How do solve xsquare+6x+5=45

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Question 246726: How do solve xsquare+6x+5=45
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+6x+5=45
x^2+6x-40=0
What are the integer factors of 40?(40,1),(20,2), (10,4), (8,5)
Which factors of 40 are 6 apart? 4, 10
We want + 6 so +10-4
(x-4)(x+10)=0
x=4
x=-10
see below for 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-40+=+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-40=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%286%29-sqrt%28+196+%29%29%2F2%5C1+=+-10

Quadratic expression 1x%5E2%2B6x%2B-40 can be factored:
1x%5E2%2B6x%2B-40+=+1%28x-4%29%2A%28x--10%29
Again, the answer is: 4, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-40+%29