SOLUTION: I have been barely introduced to the quadratic formula and solving for equations using it and was just confused on how to solve for: (x+13)(x+5)=-2 using the quadratic formula. If

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have been barely introduced to the quadratic formula and solving for equations using it and was just confused on how to solve for: (x+13)(x+5)=-2 using the quadratic formula. If       Log On


   

Question 776885: I have been barely introduced to the quadratic formula and solving for equations using it and was just confused on how to solve for: (x+13)(x+5)=-2 using the quadratic formula. If you could help me I would appreciate it :)
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
First express the problem as a quadratic equation.
%28x%2B13%29%28x%2B5%29=-2
x%2Ax%2B13%2Ax%2Bx%2A5%2B13%2A5=-2
x%5E2%2B18x%2B67=0

Now solve this quadratic equation as below.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B18x%2B67+=+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=%2818%29%5E2-4%2A1%2A67=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+56+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+56+%29%29%2F2%5C1+=+-5.25834261322606
x%5B2%5D+=+%28-%2818%29-sqrt%28+56+%29%29%2F2%5C1+=+-12.7416573867739

Quadratic expression 1x%5E2%2B18x%2B67 can be factored:
1x%5E2%2B18x%2B67+=+1%28x--5.25834261322606%29%2A%28x--12.7416573867739%29
Again, the answer is: -5.25834261322606, -12.7416573867739. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B18%2Ax%2B67+%29