SOLUTION: Solve x^2+6x=16 use the quadratic formula to find the exact solution

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Question 361946: Solve
x^2+6x=16
use the quadratic formula to find the exact solution
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

x^2+6x=16

x^2+6x-16 = 0

Solve using the quadratic formula




 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-16+=+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=%286%29%5E2-4%2A1%2A-16=100.

  

  Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+100+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%286%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+2

    x%5B2%5D+=+%28-%286%29-sqrt%28+100+%29%29%2F2%5C1+=+-8

    

    Quadratic expression 1x%5E2%2B6x%2B-16 can be factored:

  1x%5E2%2B6x%2B-16+=+1%28x-2%29%2A%28x--8%29

  Again, the answer is: 2, -8.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-16+%29