SOLUTION: x^2 + 20x = 200

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Question 143650: x^2 + 20x = 200
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to solve for x



x%5E2%2B20x=200 Start with the given equation


x%5E2%2B20x-200=0 Subtract 200 from both sides.

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 x%5E2%2B20%2Ax-200=0 ( notice a=1, b=20, and c=-200)




x+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A1%2A-200+%29%29%2F%282%2A1%29 Plug in a=1, b=20, and c=-200



x+=+%28-20+%2B-+sqrt%28+400-4%2A1%2A-200+%29%29%2F%282%2A1%29 Square 20 to get 400



x+=+%28-20+%2B-+sqrt%28+400%2B800+%29%29%2F%282%2A1%29 Multiply -4%2A-200%2A1 to get 800



x+=+%28-20+%2B-+sqrt%28+1200+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-20+%2B-+20%2Asqrt%283%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-20+%2B-+20%2Asqrt%283%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-20+%2B+20%2Asqrt%283%29%29%2F2 or x+=+%28-20+-+20%2Asqrt%283%29%29%2F2


Now break up the fraction


x=-20%2F2%2B20%2Asqrt%283%29%2F2 or x=-20%2F2-20%2Asqrt%283%29%2F2


Simplify


x=-10%2B10%2Asqrt%283%29 or x=-10-10%2Asqrt%283%29



So our answers are


x=-10%2B10%2Asqrt%283%29 or x=-10-10%2Asqrt%283%29


which approximate to


x=7.32050808 or x=-27.32050808