SOLUTION: The equation 2x^2+14x+3=0 has two solutions A and B. A= ___ and B= ___

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Question 346732: The equation 2x^2+14x+3=0 has two solutions A and B. A= ___ and B= ___
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
2x%5E2%2B14x%2B3=0
* This is an quadratic equation that can be solved applying the Quadratic Formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
A =-0.221280737849, B = -6.778719262151.
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B14x%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=%2814%29%5E2-4%2A2%2A3=172.

Discriminant d=172 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-14%2B-sqrt%28+172+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2814%29%2Bsqrt%28+172+%29%29%2F2%5C2+=+-0.221280737849
x%5B2%5D+=+%28-%2814%29-sqrt%28+172+%29%29%2F2%5C2+=+-6.778719262151

Quadratic expression 2x%5E2%2B14x%2B3 can be factored:
2x%5E2%2B14x%2B3+=+2%28x--0.221280737849%29%2A%28x--6.778719262151%29
Again, the answer is: -0.221280737849, -6.778719262151. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B14%2Ax%2B3+%29