SOLUTION: solve the quadratic equation by using the quadratic formula. 2xsquared + 4x = 1 Thank you so much.

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Question 17145: solve the quadratic equation by using the quadratic formula.
2xsquared + 4x = 1
Thank you so much.
Found 2 solutions by xcentaur, Alwayscheerful:
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
+2x%5E2+%2B+4x+-+1+=+0+
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=[-4 +- sqrt(16 - 4*2*-1)]/2(2)


x=[-4 +- sqrt(16+8)]/4


x=(-4/4) +- (sqrt(24)/4)


x=-1 +- 2sqrt(6)/4


x=-1 +- sqrt(6)/2


-Prabhat


Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
You want to move the 1 over to the left side so the equation is quadratic.
2x%5E2%2B4x-1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%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=%284%29%5E2-4%2A2%2A-1=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+24+%29%29%2F2%5C2+=+0.224744871391589
x%5B2%5D+=+%28-%284%29-sqrt%28+24+%29%29%2F2%5C2+=+-2.22474487139159

Quadratic expression 2x%5E2%2B4x%2B-1 can be factored:
2x%5E2%2B4x%2B-1+=+2%28x-0.224744871391589%29%2A%28x--2.22474487139159%29
Again, the answer is: 0.224744871391589, -2.22474487139159. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-1+%29

Hope this helps!