SOLUTION: Solve {{{x^2-5x=11}}}

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Question 145405: Solve x%5E2-5x=11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-5x=11 Start with the given equation.


x%5E2-5x-11=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=-5, and c=-11


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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-11%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-5, and c=-11


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-11%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%281%29%28-11%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25--44+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-11%29 to get -44


x+=+%285+%2B-+sqrt%28+25%2B44+%29%29%2F%282%281%29%29 Rewrite sqrt%2825--44%29 as sqrt%2825%2B44%29


x+=+%285+%2B-+sqrt%28+69+%29%29%2F%282%281%29%29 Add 25 to 44 to get 69


x+=+%285+%2B-+sqrt%28+69+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%285%2Bsqrt%2869%29%29%2F%282%29 or x+=+%285-sqrt%2869%29%29%2F%282%29 Break up the expression.


So our answers are x+=+%285%2Bsqrt%2869%29%29%2F%282%29 or x+=+%285-sqrt%2869%29%29%2F%282%29


which approximate to x=6.653 or x=-1.653