SOLUTION: What are the solutions of the quadratic equation? 4x^2 + 33x + 54 = 0

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Question 699585: What are the solutions of the quadratic equation?
4x^2 + 33x + 54 = 0
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Since the equation is set to zero, you can use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B33x%2B54+=+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=%2833%29%5E2-4%2A4%2A54=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-33%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2833%29%2Bsqrt%28+225+%29%29%2F2%5C4+=+-2.25
x%5B2%5D+=+%28-%2833%29-sqrt%28+225+%29%29%2F2%5C4+=+-6

Quadratic expression 4x%5E2%2B33x%2B54 can be factored:
4x%5E2%2B33x%2B54+=+4%28x--2.25%29%2A%28x--6%29
Again, the answer is: -2.25, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B33%2Ax%2B54+%29

So x can equal -2.25 and -6