SOLUTION: what is the value of x using the equation {{{x^2+4x-21=0}}}

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Question 254065: what is the value of x using the equation x%5E2%2B4x-21=0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+4x-21=0 is a quadratic equation.
It can be factored into
(x-3)(x+7)=0
so that its solutions (roots ) are 3 and -7
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-21+=+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=%284%29%5E2-4%2A1%2A-21=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%284%29-sqrt%28+100+%29%29%2F2%5C1+=+-7

Quadratic expression 1x%5E2%2B4x%2B-21 can be factored:
1x%5E2%2B4x%2B-21+=+1%28x-3%29%2A%28x--7%29
Again, the answer is: 3, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-21+%29