SOLUTION: Solve and show steps by completing the square: x^2+8x+13=0

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Question 184184: Solve and show steps by completing the square:
x^2+8x+13=0
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B8x%2B13 Start with the given expression.


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%2B13 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%2B13 Group the first three terms.


%28x%2B4%29%5E2-16%2B13 Factor x%5E2%2B8x%2B16 to get %28x%2B4%29%5E2.


%28x%2B4%29%5E2-3 Combine like terms.


So after completing the square, x%5E2%2B8x%2B13 transforms to %28x%2B4%29%5E2-3. So x%5E2%2B8x%2B13=%28x%2B4%29%5E2-3.


So x%5E2%2B8x%2B13=0 is equivalent to %28x%2B4%29%5E2-3=0.


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Now let's solve %28x%2B4%29%5E2-3=0


%28x%2B4%29%5E2-3=0 Start with the given equation.


%28x%2B4%29%5E2=0%2B3Add 3 to both sides.


%28x%2B4%29%5E2=3 Combine like terms.


x%2B4=0%2B-sqrt%283%29 Take the square root of both sides.


x%2B4=sqrt%283%29 or x%2B4=-sqrt%283%29 Break up the "plus/minus" to form two equations.


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


x=-4%2Bsqrt%283%29 or x=-4-sqrt%283%29 Subtract 4 from both sides.


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Answer:


So the solutions are x=-4%2Bsqrt%283%29 or x=-4-sqrt%283%29.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Move the constant term to the right side:



Divide the coefficient on the x term by 2 and square the result. Add this result to both sides. 8 divided by 2 is 4 squared is 16:



You now have a perfect square on the left, factor it:



Take the square root of both sides, remembering to consider both the positive and negative root:



Solve for x:



John