SOLUTION: Solve the equation using the quadratic formula. 2x^2 = 30

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Question 247381: Solve the equation using the quadratic formula.
2x^2 = 30
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2+=+30 is not in the form to solve using the quadratic equation. You have to get it organized in standard form.
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Subtract 30 from both sides.
2x%5E2+-+30+=+0
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Dividing both sides by 2.
x%5E2+-+15+=+0
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Obviously, this is a parabola that is centered on the y-axis and crosses the y-axis at -15.
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Can this be factored? Yes.
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%28x+%2B+sqrt%2815%29%29%28x+-+sqrt%2815%29%29+=+0
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Perhaps odd looking, but not unreasonable. Or you can use the quadratic:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-15+=+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%29%5E2-4%2A1%2A-15=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+60+%29%29%2F2%5C1+=+3.87298334620742
x%5B2%5D+=+%28-%280%29-sqrt%28+60+%29%29%2F2%5C1+=+-3.87298334620742

Quadratic expression 1x%5E2%2B0x%2B-15 can be factored:
1x%5E2%2B0x%2B-15+=+1%28x-3.87298334620742%29%2A%28x--3.87298334620742%29
Again, the answer is: 3.87298334620742, -3.87298334620742. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-15+%29