SOLUTION: xsquared+x-5

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Question 170864: xsquared+x-5
Found 2 solutions by KnightOwlTutor, jim_thompson5910:
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-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=%281%29%5E2-4%2A1%2A-5=21.

Discriminant d=21 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+21+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+21+%29%29%2F2%5C1+=+1.79128784747792
x%5B2%5D+=+%28-%281%29-sqrt%28+21+%29%29%2F2%5C1+=+-2.79128784747792

Quadratic expression 1x%5E2%2B1x%2B-5 can be factored:
1x%5E2%2B1x%2B-5+=+1%28x-1.79128784747792%29%2A%28x--2.79128784747792%29
Again, the answer is: 1.79128784747792, -2.79128784747792. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-5+%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to solve x%5E2%2Bx-5=0


x%5E2%2Bx-5=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=1, and c=-5


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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Plug in a=1, b=1, and c=-5


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-5%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--20+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-5%29 to get -20


x+=+%28-1+%2B-+sqrt%28+1%2B20+%29%29%2F%282%281%29%29 Rewrite sqrt%281--20%29 as sqrt%281%2B20%29


x+=+%28-1+%2B-+sqrt%28+21+%29%29%2F%282%281%29%29 Add 1 to 20 to get 21


x+=+%28-1+%2B-+sqrt%28+21+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1%2Bsqrt%2821%29%29%2F%282%29 or x+=+%28-1-sqrt%2821%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%28-1%2Bsqrt%2821%29%29%2F%282%29 or x+=+%28-1-sqrt%2821%29%29%2F%282%29


which approximate to x=1.791 or x=-2.791