SOLUTION: Solve -5x^2 + 10x = -3

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Question 227577: Solve -5x^2 + 10x = -3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-5x%5E2%2B10x=-3 Start with the given equation.


-5x%5E2%2B10x%2B3=0 Add 3 to both sides.


Notice that the quadratic -5x%5E2%2B10x%2B3 is in the form of Ax%5E2%2BBx%2BC where A=-5, B=10, and C=3


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%28-5%29%283%29+%29%29%2F%282%28-5%29%29 Plug in A=-5, B=10, and C=3


x+=+%28-10+%2B-+sqrt%28+100-4%28-5%29%283%29+%29%29%2F%282%28-5%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100--60+%29%29%2F%282%28-5%29%29 Multiply 4%28-5%29%283%29 to get -60


x+=+%28-10+%2B-+sqrt%28+100%2B60+%29%29%2F%282%28-5%29%29 Rewrite sqrt%28100--60%29 as sqrt%28100%2B60%29


x+=+%28-10+%2B-+sqrt%28+160+%29%29%2F%282%28-5%29%29 Add 100 to 60 to get 160


x+=+%28-10+%2B-+sqrt%28+160+%29%29%2F%28-10%29 Multiply 2 and -5 to get -10.


x+=+%28-10+%2B-+4%2Asqrt%2810%29%29%2F%28-10%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-10%2B4%2Asqrt%2810%29%29%2F%28-10%29 or x+=+%28-10-4%2Asqrt%2810%29%29%2F%28-10%29 Break up the expression.


x+=+%285-2%2Asqrt%2810%29%29%2F%285%29 or x+=+%285%2B2%2Asqrt%2810%29%29%2F%285%29 Reduce.


So the solutions are x+=+%285-2%2Asqrt%2810%29%29%2F%285%29 or x+=+%285%2B2%2Asqrt%2810%29%29%2F%285%29


which approximate to x=-0.265 or x=2.265