SOLUTION: (3x+1)(x-1)= -3x

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Question 167447: (3x+1)(x-1)= -3x
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
(3x+1)(x-1)= -3x
FOIL the left:
3x^2 - 3x + x - 1 = -3x
3x^2 - 2x - 1 = -3x
3x^2 + x - 1 = 0
.
Solving using the quadratic equation yields:
x = {0.4343, -0.7676}
.
Details of quadratic:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B1x%2B-1+=+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=%281%29%5E2-4%2A3%2A-1=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+0.434258545910665
x%5B2%5D+=+%28-%281%29-sqrt%28+13+%29%29%2F2%5C3+=+-0.767591879243998

Quadratic expression 3x%5E2%2B1x%2B-1 can be factored:
3x%5E2%2B1x%2B-1+=+3%28x-0.434258545910665%29%2A%28x--0.767591879243998%29
Again, the answer is: 0.434258545910665, -0.767591879243998. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B1%2Ax%2B-1+%29