SOLUTION: Could you help by Solving this equation by using the Quadratic Formula:? {{{ (1/4) x^2 + (1/4) x -1/2 =0 }}} IS the answer x=1 x=-2 ? Thank you

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Question 1042032: Could you help by Solving this equation by using the Quadratic Formula:?
+%281%2F4%29+x%5E2+%2B+%281%2F4%29+x+-1%2F2+=0+
IS the answer x=1 x=-2
?
Thank you

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+%281%2F4%29+x%5E2+%2B+%281%2F4%29+x+-1%2F2+=0+
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.25x%5E2%2B0.25x%2B-0.5+=+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=%280.25%29%5E2-4%2A0.25%2A-0.5=0.5625.

Discriminant d=0.5625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.25%2B-sqrt%28+0.5625+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280.25%29%2Bsqrt%28+0.5625+%29%29%2F2%5C0.25+=+1
x%5B2%5D+=+%28-%280.25%29-sqrt%28+0.5625+%29%29%2F2%5C0.25+=+-2

Quadratic expression 0.25x%5E2%2B0.25x%2B-0.5 can be factored:
0.25x%5E2%2B0.25x%2B-0.5+=+%28x-1%29%2A%28x--2%29
Again, the answer is: 1, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.25%2Ax%5E2%2B0.25%2Ax%2B-0.5+%29

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x%5E2+%2B+x+-+2+=0+
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-2+=+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%2A1%2A-2=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+9+%29%29%2F2%5C1+=+1
x%5B2%5D+=+%28-%281%29-sqrt%28+9+%29%29%2F2%5C1+=+-2

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

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Instead of asking this question, you can simply substitute these values of x into the left side quadratic polynomial and check.