SOLUTION: solve: x^2-x-40=2

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Question 555479: solve:
x^2-x-40=2
Answer by jim_thompson5910(35256) About Me  (Show Source):
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x%5E2-x-40=2 Start with the given equation.


x%5E2-x-40-2=0 Get every term to the left side.


x%5E2-x-42=0 Combine like terms.


Notice that the quadratic x%5E2-x-42 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-1, and C=-42


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-42%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=-42


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-42%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-42%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--168+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-42%29 to get -168


x+=+%281+%2B-+sqrt%28+1%2B168+%29%29%2F%282%281%29%29 Rewrite sqrt%281--168%29 as sqrt%281%2B168%29


x+=+%281+%2B-+sqrt%28+169+%29%29%2F%282%281%29%29 Add 1 to 168 to get 169


x+=+%281+%2B-+sqrt%28+169+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+13%29%2F%282%29 Take the square root of 169 to get 13.


x+=+%281+%2B+13%29%2F%282%29 or x+=+%281+-+13%29%2F%282%29 Break up the expression.


x+=+%2814%29%2F%282%29 or x+=++%28-12%29%2F%282%29 Combine like terms.


x+=+7 or x+=+-6 Simplify.


So the solutions are x+=+7 or x+=+-6


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