SOLUTION: Solve quadratic equation by using the quadratic formula. x2-x-6=0

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Question 84850: Solve quadratic equation by using the quadratic formula.
x2-x-6=0
Found 2 solutions by jim_thompson5910, Spec80:
Answer by jim_thompson5910(21680) 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%2B-1x%2B-6+=+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%2A-6=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-1%29-sqrt%28+25+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B-1x%2B-6 can be factored:
1x%5E2%2B-1x%2B-6+=+1%28x-3%29%2A%28x--2%29
Again, the answer is: 3, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-6+%29

Answer by Spec80(9) About Me  (Show Source):
You can put this solution on YOUR website!
So first the quadratic formula is:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
For our problem, it says x%5E2-x%2B6=0 . The generaly formula for the quadratic equation is +ax%5E2+%2B+bx+%2B+c+=0 therefore it means that in our case, a=1 , b= -1, and c=6 .
From here, we can plug these values into the formula to make it look like:
%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29+
When we simplfy this we first get:
+1+%2B-+sqrt%28%281-24%29%29%2F%282%2A1%29+
At this point it becomes clear that your problem does not have a solution since we cannot take the sqrt%28-23%29 because we cannot take the square root of negative numbers.