SOLUTION: Give the exact and approximate solutions to three decimal places. x^2-7x+7=0

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Question 299575: Give the exact and approximate solutions to three decimal places.
x^2-7x+7=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-7x%2B7=0 Start with the given equation.


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


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%281%29%287%29+%29%29%2F%282%281%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49-28+%29%29%2F%282%281%29%29 Multiply 4%281%29%287%29 to get 28


x+=+%287+%2B-+sqrt%28+21+%29%29%2F%282%281%29%29 Subtract 28 from 49 to get 21


x+=+%287+%2B-+sqrt%28+21+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%287%2Bsqrt%2821%29%29%2F%282%29 or x+=+%287-sqrt%2821%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%287%2Bsqrt%2821%29%29%2F%282%29 or x+=+%287-sqrt%2821%29%29%2F%282%29