SOLUTION: find the exact solutions to 5x^2+17x+6=0

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Question 76944: find the exact solutions to 5x^2+17x+6=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.
Error occurred executing solver 'quadratic_factoring' .


So our quadratic factors to:
%285x%2B2%29%28x%2B3%29=0
Now set each factor equal to zero
5x%2B2=0
5x=-2
x=-2%2F5
x%2B3=0
x=-3
So our answers are
x=-2%2F5 or x=-3


or you could use the quadratic formula to solve for x:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B17x%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=%2817%29%5E2-4%2A5%2A6=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-17%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2817%29%2Bsqrt%28+169+%29%29%2F2%5C5+=+-0.4
x%5B2%5D+=+%28-%2817%29-sqrt%28+169+%29%29%2F2%5C5+=+-3

Quadratic expression 5x%5E2%2B17x%2B6 can be factored:
5x%5E2%2B17x%2B6+=+5%28x--0.4%29%2A%28x--3%29
Again, the answer is: -0.4, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B17%2Ax%2B6+%29