SOLUTION: x^2-7x+11=0 the exact solutions=? the approximate solutions to 3 decimal places are?

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Question 206085: x^2-7x+11=0
the exact solutions=?
the approximate solutions to 3 decimal places are?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-7x%2B11=0 Start with the given equation.


Notice that the quadratic x%5E2-7x%2B11 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-7, and C=11


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%2811%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-7, and C=11


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%2811%29+%29%29%2F%282%281%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%281%29%2811%29+%29%29%2F%282%281%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49-44+%29%29%2F%282%281%29%29 Multiply 4%281%29%2811%29 to get 44


x+=+%287+%2B-+sqrt%28+5+%29%29%2F%282%281%29%29 Subtract 44 from 49 to get 5


x+=+%287+%2B-+sqrt%28+5+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%287%2Bsqrt%285%29%29%2F%282%29 or x+=+%287-sqrt%285%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%287%2Bsqrt%285%29%29%2F%282%29 or x+=+%287-sqrt%285%29%29%2F%282%29


which approximate to x=4.618 or x=2.382


Note: use a calculator to evaluate %287%2Bsqrt%285%29%29%2F%282%29 and %287-sqrt%285%29%29%2F%282%29 to get the approximate answers.