SOLUTION: Solve by using the quadratic formula 5x^2 + x = 3

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Question 104365: Solve by using the quadratic formula 5x^2 + x = 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2+%2B+x+=+3 Start with the given equation


5x%5E2+%2B+x+-3=0 Subtract 3 from both sides


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 5%2Ax%5E2%2Bx-3=0 ( notice a=5, b=1, and c=-3)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A5%2A-3+%29%29%2F%282%2A5%29 Plug in a=5, b=1, and c=-3




x+=+%28-1+%2B-+sqrt%28+1-4%2A5%2A-3+%29%29%2F%282%2A5%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B60+%29%29%2F%282%2A5%29 Multiply -4%2A-3%2A5 to get 60




x+=+%28-1+%2B-+sqrt%28+61+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+sqrt%2861%29%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+sqrt%2861%29%29%2F10 Multiply 2 and 5 to get 10


So now the expression breaks down into two parts


x+=+%28-1+%2B+sqrt%2861%29%29%2F10 or x+=+%28-1+-+sqrt%2861%29%29%2F10



Now break up the fraction



x=-1%2F10%2Bsqrt%2861%29%2F10 or x=-1%2F10-sqrt%2861%29%2F10



Simplify



x=-1%2F10%2Bsqrt%2861%29%2F10 or x=-1%2F10-sqrt%2861%29%2F10



So the solutions are:

x=-1%2F10%2Bsqrt%2861%29%2F10 or x=-1%2F10-sqrt%2861%29%2F10