SOLUTION: what does "x" equal? (x+1)(x-3)=4 What does "x" equal? x(x-2)= -6

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Question 39154: what does "x" equal?
(x+1)(x-3)=4

What does "x" equal?
x(x-2)= -6
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B1%29%28x-3%29=4
x%5E2-2x-3=4
x%5E2-2x-7=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-7+=+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=%28-2%29%5E2-4%2A1%2A-7=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+32+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+32+%29%29%2F2%5C1+=+3.82842712474619
x%5B2%5D+=+%28-%28-2%29-sqrt%28+32+%29%29%2F2%5C1+=+-1.82842712474619

Quadratic expression 1x%5E2%2B-2x%2B-7 can be factored:
1x%5E2%2B-2x%2B-7+=+1%28x-3.82842712474619%29%2A%28x--1.82842712474619%29
Again, the answer is: 3.82842712474619, -1.82842712474619. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-7+%29

x(x-2)= -6
x%5E2+-+2x+%2B+6+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B6+=+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=%28-2%29%5E2-4%2A1%2A6=-20.

The discriminant -20 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 -20 is + or - sqrt%28+20%29+=+4.47213595499958.

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-2%2Ax%2B6+%29