SOLUTION: Solve : {{{-5x^2+5=-2x }}}

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Question 597807: Solve : -5x%5E2%2B5=-2x+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-5x%5E2%2B5=-2x+ Start with the given equation

-5x%5E2%2B5%2B2x+=+0+ Add 2x to both sides.

-5x%5E2%2B2x%2B5+=+0+ Rearrange the terms.

5x%5E2-2x-5+=+0+ Multiply every term by -1 to make the leading coefficient positive.

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


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%285%29%28-5%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-2, and C=-5


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%285%29%28-5%29+%29%29%2F%282%285%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%285%29%28-5%29+%29%29%2F%282%285%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--100+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-5%29 to get -100


x+=+%282+%2B-+sqrt%28+4%2B100+%29%29%2F%282%285%29%29 Rewrite sqrt%284--100%29 as sqrt%284%2B100%29


x+=+%282+%2B-+sqrt%28+104+%29%29%2F%282%285%29%29 Add 4 to 100 to get 104


x+=+%282+%2B-+sqrt%28+104+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%282+%2B-+2%2Asqrt%2826%29%29%2F%2810%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%2B2%2Asqrt%2826%29%29%2F%2810%29 or x+=+%282-2%2Asqrt%2826%29%29%2F%2810%29 Break up the expression.


x+=+%281%2Bsqrt%2826%29%29%2F%285%29 or x+=+%281-sqrt%2826%29%29%2F%285%29 Reduce


So the solutions are x+=+%281%2Bsqrt%2826%29%29%2F%285%29 or x+=+%281-sqrt%2826%29%29%2F%285%29