SOLUTION: Solve: x^2+ 5x+ 3= 0

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Question 296166: Solve: x^2+ 5x+ 3= 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For more help, check out this quadratic formula solver.

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B5%2Ax%2B3=0 ( notice a=1, b=5, and c=3)





x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=3




x+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A3+%29%29%2F%282%2A1%29 Square 5 to get 25




x+=+%28-5+%2B-+sqrt%28+25%2B-12+%29%29%2F%282%2A1%29 Multiply -4%2A3%2A1 to get -12




x+=+%28-5+%2B-+sqrt%28+13+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-5+%2B-+sqrt%2813%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-5+%2B-+sqrt%2813%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-5+%2B+sqrt%2813%29%29%2F2 or x+=+%28-5+-+sqrt%2813%29%29%2F2



Now break up the fraction



x=-5%2F2%2Bsqrt%2813%29%2F2 or x=-5%2F2-sqrt%2813%29%2F2



Simplify



x=-5%2F2%2Bsqrt%2813%29%2F2 or x=-5%2F2-sqrt%2813%29%2F2



So the solutions are:

x=-5%2F2%2Bsqrt%2813%29%2F2 or x=-5%2F2-sqrt%2813%29%2F2