SOLUTION: Solve using the quadratic formula: x^2 – 3x = 7x – 2

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Question 147431: Solve using the quadratic formula:
x^2 – 3x = 7x – 2
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula:
x^2 – 3x = 7x – 2
.
First, move all the terms to the left side:
x^2 – 3x = 7x – 2
subtracting 7x from both sides:
x^2 – 10x = –2
adding 2 to both sides:
x^2 – 10x + 2 = 0
.
Now, we can apply the quadratic equation:
solution: x = (9.796, 0.204)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-10x%2B2+=+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=%28-10%29%5E2-4%2A1%2A2=92.

Discriminant d=92 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+92+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+92+%29%29%2F2%5C1+=+9.79583152331272
x%5B2%5D+=+%28-%28-10%29-sqrt%28+92+%29%29%2F2%5C1+=+0.204168476687281

Quadratic expression 1x%5E2%2B-10x%2B2 can be factored:
1x%5E2%2B-10x%2B2+=+1%28x-9.79583152331272%29%2A%28x-0.204168476687281%29
Again, the answer is: 9.79583152331272, 0.204168476687281. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B2+%29