SOLUTION: x^2-x=72

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Question 571239: x^2-x=72
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x=72 Start with the given equation.


x%5E2-x-72=0 Get every term to the left side.


Notice that the quadratic x%5E2-x-72 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-1, and C=-72


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%28-72%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=-72


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--288+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-72%29 to get -288


x+=+%281+%2B-+sqrt%28+1%2B288+%29%29%2F%282%281%29%29 Rewrite sqrt%281--288%29 as sqrt%281%2B288%29


x+=+%281+%2B-+sqrt%28+289+%29%29%2F%282%281%29%29 Add 1 to 288 to get 289


x+=+%281+%2B-+sqrt%28+289+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+17%29%2F%282%29 Take the square root of 289 to get 17.


x+=+%281+%2B+17%29%2F%282%29 or x+=+%281+-+17%29%2F%282%29 Break up the expression.


x+=+%2818%29%2F%282%29 or x+=++%28-16%29%2F%282%29 Combine like terms.


x+=+9 or x+=+-8 Simplify.


So the solutions are x+=+9 or x+=+-8