SOLUTION: I need to solve x^2+6x-16=0 by completing the square

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Question 600305: I need to solve x^2+6x-16=0 by completing the square
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's complete the square.



x%5E2%2B6x-16 Start with the given expression.


Take half of the x coefficient 6 to get 3. In other words, %281%2F2%29%286%29=3.


Now square 3 to get 9. In other words, %283%29%5E2=%283%29%283%29=9


x%5E2%2B6x%2Bhighlight%289-9%29-16 Now add and subtract 9. Make sure to place this after the "x" term. Notice how 9-9=0. So the expression is not changed.


%28x%5E2%2B6x%2B9%29-9-16 Group the first three terms.


%28x%2B3%29%5E2-9-16 Factor x%5E2%2B6x%2B9 to get %28x%2B3%29%5E2.


%28x%2B3%29%5E2-25 Combine like terms.


So after completing the square, x%5E2%2B6x-16 transforms to %28x%2B3%29%5E2-25. So x%5E2%2B6x-16=%28x%2B3%29%5E2-25.


So x%5E2%2B6x-16=0 is equivalent to %28x%2B3%29%5E2-25=0.


Now let's solve %28x%2B3%29%5E2-25=0



%28x%2B3%29%5E2-25=0 Start with the given equation.


%28x%2B3%29%5E2=25 Add 25 to both sides


x%2B3=%22%22%2B-sqrt%2825%29 Take the square root of both sides.


x%2B3=sqrt%2825%29 or x%2B3=-sqrt%2825%29 Break up the "plus/minus" to form two equations.


x%2B3=5 or x%2B3=-5 Take the square root of 25 to get 5.


x=-3%2B5 or x=-3-5 Subtract 3 from both sides.


x=2 or x=-8 Combine like terms.


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Answer:


So the solutions are x=2 or x=-8.