SOLUTION: solve for x: {{{ -5x^2= 12-3x }}}

Algebra ->  Equations -> SOLUTION: solve for x: {{{ -5x^2= 12-3x }}}      Log On


   

Question 592834: solve for x: +-5x%5E2=+12-3x+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+-5x%5E2=+12-3x+ Start with the given equation.


+0=+12-3x%2B5x%5E2+ Add 5x%5E2 to both sides


0+=+5x%5E2-3x%2B12 Rearrange the terms.


5x%5E2-3x%2B12+=+0 Flip the equation.


Notice that the quadratic 5x%5E2-3x%2B12 is in the form of Ax%5E2%2BBx%2BC where A=5, B=-3, and C=12


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%2812%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-3, and C=12


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%2812%29+%29%29%2F%282%285%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%285%29%2812%29+%29%29%2F%282%285%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9-240+%29%29%2F%282%285%29%29 Multiply 4%285%29%2812%29 to get 240


x+=+%283+%2B-+sqrt%28+-231+%29%29%2F%282%285%29%29 Subtract 240 from 9 to get -231


x+=+%283+%2B-+sqrt%28+-231+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%283+%2B-+i%2Asqrt%28231%29%29%2F%2810%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%283%2Bi%2Asqrt%28231%29%29%2F%2810%29 or x+=+%283-i%2Asqrt%28231%29%29%2F%2810%29 Break up the expression.


So the solutions are x+=+%283%2Bi%2Asqrt%28231%29%29%2F%2810%29 or x+=+%283-i%2Asqrt%28231%29%29%2F%2810%29