SOLUTION: Use the quadratic formula to solve the equation., x^2-x=-2 Thank you!

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Question 224805: Use the quadratic formula to solve the equation.,
x^2-x=-2
Thank you!
Found 2 solutions by checkley77, drj:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-x=-2
x^2-x-2=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(1+-sqrt[-1^2-4*1*-2])/2*1
x=(1+-sqrt[1+8])/2
x=(1+-sqrt9)/2
x=(1+-3)/2
x=(1+3)/2
x=4/2
x=2 ans.
x=(1-3)/2
x=-2/2
x=-1 ans.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Use the quadratic formula to solve the equation.

x%5E2-x=-2

Step 1. Put the equation in proper form as follows:

Add 2 to both sides of the equation to get

x%5E2-x%2B2=-2%2B2

x%5E2-x%2B2=0
Step 2. The quadratic formula is given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=-1, and c=2.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%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=%28-1%29%5E2-4%2A1%2A2=-7.

The discriminant -7 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 -7 is + or - sqrt%28+7%29+=+2.64575131106459.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B2+%29



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Good luck in your studies!

Respectfully,
Dr J