SOLUTION: Please solve the equation using the quadratic formula. Thanks! 2x^2=-6x-3

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Question 976212: Please solve the equation using the quadratic formula. Thanks!
2x^2=-6x-3
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please solve the equation using the quadratic formula. Thanks!
2x^2=-6x-3
2x%5E2+%2B+6x+%2B+3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B6x%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=%286%29%5E2-4%2A2%2A3=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+12+%29%29%2F2%5C2+=+-0.633974596215561
x%5B2%5D+=+%28-%286%29-sqrt%28+12+%29%29%2F2%5C2+=+-2.36602540378444

Quadratic expression 2x%5E2%2B6x%2B3 can be factored:
2x%5E2%2B6x%2B3+=+%28x--0.633974596215561%29%2A%28x--2.36602540378444%29
Again, the answer is: -0.633974596215561, -2.36602540378444. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B6%2Ax%2B3+%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2 = -6x -3
-2x^2 -6x -3 = 0
x^2 + 3x + 1.5 = 0
a = 1, b = 3, c = 1.5
x = (-b + or - sqrt(b^2 - 4ac)) / 2a
x = (-3 + or - sqrt(9 - 4(1)(1.5)) / 2)
x = (-3 + or - sqrt(3)) / 2
x = (-3 + 1.732050808 ) / 2 = −0.633974596 approx -0.633975
x = (-3 - 1.732050808 ) / 2 = −2.366025404 approx -2.36603