SOLUTION: -x Squared + 2x = 8

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: -x Squared + 2x = 8       Log On


   

Question 145102: -x Squared + 2x = 8
Found 2 solutions by shahid, jim_thompson5910:
Answer by shahid(44) About Me  (Show Source):
You can put this solution on YOUR website!
-x%5E2%2B2x=8
-%28x%5E2-2x%29=8 taking minus sign common
x%5E2-2x=-8 dividing by -1 both sides
x%5E2-2x%2B8=0
x%5E2-4x%2B2x-8=0 breaking middle term
%28x-4%29%2A%28x%2B2%29=0
x=4 or x=-2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-x%5E2%2B+2x+=+8 Start with the given equation.


-x%5E2%2B+2x+-8=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-1, b=2, and c=-8


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-%282%29+%2B-+sqrt%28+%282%29%5E2-4%28-1%29%28-8%29+%29%29%2F%282%28-1%29%29 Plug in a=-1, b=2, and c=-8


x+=+%28-2+%2B-+sqrt%28+4-4%28-1%29%28-8%29+%29%29%2F%282%28-1%29%29 Square 2 to get 4.


x+=+%28-2+%2B-+sqrt%28+4-32+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28-8%29 to get 32


x+=+%28-2+%2B-+sqrt%28+-28+%29%29%2F%282%28-1%29%29 Subtract 32 from 4 to get -28


x+=+%28-2+%2B-+sqrt%28+-28+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%28-2+%2B-+2i%2Asqrt%287%29%29%2F%28-2%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-2%29%2F%28-2%29+%2B-+%282i%2Asqrt%287%29%29%2F%28-2%29 Break up the fraction.


x+=+1+%2B-+-1sqrt%287%29%2Ai Reduce.


x+=+1-1sqrt%287%29%2Ai or x+=+1%2B1sqrt%287%29%2Ai Break up the expression.


So our answers are x+=+1-1sqrt%287%29%2Ai or x+=+1%2B1sqrt%287%29%2Ai


which approximate to x=-1.646%2Ai or x=3.646%2Ai