SOLUTION: Solve the equation using the quadratic formula. 2x^2 + 10x + 3 = 0

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Question 185410: Solve the equation using the quadratic formula.
2x^2 + 10x + 3 = 0
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2 + 10x + 3 = 0
Applying the quadratic yields:
x = {-0.321, -4.679}
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Details below:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B10x%2B3+=+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=%2810%29%5E2-4%2A2%2A3=76.

Discriminant d=76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+76+%29%29%2F2%5C2+=+-0.320550528229663
x%5B2%5D+=+%28-%2810%29-sqrt%28+76+%29%29%2F2%5C2+=+-4.67944947177034

Quadratic expression 2x%5E2%2B10x%2B3 can be factored:
2x%5E2%2B10x%2B3+=+2%28x--0.320550528229663%29%2A%28x--4.67944947177034%29
Again, the answer is: -0.320550528229663, -4.67944947177034. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B10%2Ax%2B3+%29