SOLUTION: -x^2+4x=7

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Question 297087: -x^2+4x=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-x%5E2%2B4x=7 Start with the given equation.


-x%5E2%2B4x-7=0 Subtract 7 from both sides.


x%5E2-4x%2B7=0 Multiply every term by -1 to make the leading coefficient positive.


Notice that the quadratic x%5E2-4x%2B7 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-4, and C=7


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-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-4, and C=7


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%281%29%287%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-28+%29%29%2F%282%281%29%29 Multiply 4%281%29%287%29 to get 28


x+=+%284+%2B-+sqrt%28+-12+%29%29%2F%282%281%29%29 Subtract 28 from 16 to get -12


x+=+%284+%2B-+sqrt%28+-12+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%284+%2B-+2i%2Asqrt%283%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%284%29%2F%282%29+%2B-+%282i%2Asqrt%283%29%29%2F%282%29 Break up the fraction.


x+=+2+%2B-+sqrt%283%29%2Ai Reduce.


x+=+2%2Bsqrt%283%29%2Ai or x+=+2-sqrt%283%29%2Ai Break up the expression.


So the solutions are x+=+2%2Bsqrt%283%29%2Ai or x+=+2-sqrt%283%29%2Ai