SOLUTION: X^2-13x-12=0 what is x?

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Question 549931: X^2-13x-12=0
what is x?
Found 2 solutions by jim_thompson5910, nerdybill:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-13x-12=0 Start with the given equation.


Notice that the quadratic x%5E2-13x-12 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-13, and C=-12


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-13, and C=-12


x+=+%2813+%2B-+sqrt%28+%28-13%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Negate -13 to get 13.


x+=+%2813+%2B-+sqrt%28+169-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square -13 to get 169.


x+=+%2813+%2B-+sqrt%28+169--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%2813+%2B-+sqrt%28+169%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%28169--48%29 as sqrt%28169%2B48%29


x+=+%2813+%2B-+sqrt%28+217+%29%29%2F%282%281%29%29 Add 169 to 48 to get 217


x+=+%2813+%2B-+sqrt%28+217+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2813%2Bsqrt%28217%29%29%2F%282%29 or x+=+%2813-sqrt%28217%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%2813%2Bsqrt%28217%29%29%2F%282%29 or x+=+%2813-sqrt%28217%29%29%2F%282%29

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
X^2-13x-12=0
Since you can't factor, you can apply the "quadratic formula" to get:
x = {13.87, -0.87}
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-13x%2B-12+=+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=%28-13%29%5E2-4%2A1%2A-12=217.

Discriminant d=217 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+217+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+217+%29%29%2F2%5C1+=+13.8654599313281
x%5B2%5D+=+%28-%28-13%29-sqrt%28+217+%29%29%2F2%5C1+=+-0.865459931328117

Quadratic expression 1x%5E2%2B-13x%2B-12 can be factored:
1x%5E2%2B-13x%2B-12+=+1%28x-13.8654599313281%29%2A%28x--0.865459931328117%29
Again, the answer is: 13.8654599313281, -0.865459931328117. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-13%2Ax%2B-12+%29