SOLUTION: x(x-1)=2x-7

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Question 299442: x(x-1)=2x-7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%28x-1%29=2x-7 Start with the given equation.


x%5E2-x=2x-7 Distribute


x%5E2-x-2x%2B7=0 Get every term to the left side.


x%5E2-3x%2B7=0 Combine like terms.


Notice that the quadratic x%5E2-3x%2B7 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-3, 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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-3, and C=7


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%281%29%287%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9-28+%29%29%2F%282%281%29%29 Multiply 4%281%29%287%29 to get 28


x+=+%283+%2B-+sqrt%28+-19+%29%29%2F%282%281%29%29 Subtract 28 from 9 to get -19


x+=+%283+%2B-+sqrt%28+-19+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%283+%2B-+i%2Asqrt%2819%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%283%2Bi%2Asqrt%2819%29%29%2F%282%29 or x+=+%283-i%2Asqrt%2819%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%283%2Bi%2Asqrt%2819%29%29%2F%282%29 or x+=+%283-i%2Asqrt%2819%29%29%2F%282%29