SOLUTION: Use completing the square to solve x²+8x-11=0

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Question 173222: Use completing the square to solve x²+8x-11=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B8x-11 Start with the given left side of the given equation.


Take half of the x coefficient 8 to get 4. In other words, %281%2F2%29%288%29=4.


Now square 4 to get 16. In other words, %284%29%5E2=%284%29%284%29=16


x%5E2%2B8x%2Bhighlight%2816-16%29-11 Now add and subtract 16. Make sure to place this after the "x" term. Notice how 16-16=0. So the expression is not changed.


%28x%5E2%2B8x%2B16%29-16-11 Group the first three terms.


%28x%2B4%29%5E2-16-11 Factor x%5E2%2B8x%2B16 to get %28x%2B4%29%5E2.


%28x%2B4%29%5E2-27 Combine like terms.


So after completing the square, x%5E2%2B8x-11 transforms to %28x%2B4%29%5E2-27. So x%5E2%2B8x-11=%28x%2B4%29%5E2-27.


So x%5E2%2B8x-11=0 is equivalent to %28x%2B4%29%5E2-27=0.


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%28x%2B4%29%5E2-27=0 Start with the given equation.


%28x%2B4%29%5E2=0%2B27Add 27 to both sides.


%28x%2B4%29%5E2=27 Combine like terms.


x%2B4=0%2B-sqrt%2827%29 Take the square root of both sides.


x%2B4=sqrt%2827%29 or x%2B4=-sqrt%2827%29 Break up the "plus/minus" to form two equations.


x%2B4=3%2Asqrt%283%29 or x%2B4=-3%2Asqrt%283%29 Simplify the square root.


x=-4%2B3%2Asqrt%283%29 or x=-4-3%2Asqrt%283%29 Subtract 4 from both sides.


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Answer:


So the solutions are x=-4%2B3%2Asqrt%283%29 or x=-4-3%2Asqrt%283%29.