SOLUTION: solutions for x2 + 10x + 1 = -12 + 2x

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Question 256251: solutions for x2 + 10x + 1 = -12 + 2x
Found 2 solutions by Greenfinch, richwmiller:
Answer by Greenfinch(383) About Me  (Show Source):
You can put this solution on YOUR website!
I am assuming the equation is x^2 + 10x +1 = 2x - 12
If it is then x^2 + 8x + 13 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B13+=+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=%288%29%5E2-4%2A1%2A13=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+-2.26794919243112
x%5B2%5D+=+%28-%288%29-sqrt%28+12+%29%29%2F2%5C1+=+-5.73205080756888

Quadratic expression 1x%5E2%2B8x%2B13 can be factored:
1x%5E2%2B8x%2B13+=+1%28x--2.26794919243112%29%2A%28x--5.73205080756888%29
Again, the answer is: -2.26794919243112, -5.73205080756888. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B13+%29

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
That simplifies to x^2+8x+13 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B8x%2B13+=+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=%288%29%5E2-4%2A2%2A13=-40.

The discriminant -40 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -40 is + or - sqrt%28+40%29+=+6.32455532033676.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B8%2Ax%2B13+%29