SOLUTION: Solve 11( x - 2) + ( x - 5)= (x + 2)( x + 6)

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Question 311425: Solve
11( x - 2) + ( x - 5)= (x + 2)( x + 6)
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
11%28+x+-+2%29+%2B+%28+x+-+5%29=+%28x+%2B+2%29%28+x+%2B+6%29
11x-22+%2Bx+-5+=+x%5E2+%2B+6x+%2B+2x+%2B+12
12x+-27+=+x%5E2+%2B+8x+%2B+12
0+=+x%5E2+-+4x+%2B+39
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B39+=+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=%28-4%29%5E2-4%2A1%2A39=-140.

The discriminant -140 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 -140 is + or - sqrt%28+140%29+=+11.8321595661992.

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-4%2Ax%2B39+%29