SOLUTION: Can you please show me how to work this quadratic equation by completing the square x^2 + 4x - 12 = 0

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Question 169987: Can you please show me how to work this quadratic equation by completing the square
x^2 + 4x - 12 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B4x-12 Start with the left side of the equation.


Take half of the x coefficient 4 to get 2. In other words, %281%2F2%29%284%29=2.


Now square 2 to get 4. In other words, %282%29%5E2=%282%29%282%29=4


x%5E2%2B4x%2Bhighlight%284-4%29-12 Now add and subtract 4. Make sure to place this after the "x" term. Notice how 4-4=0. So the expression is not changed.


%28x%5E2%2B4x%2B4%29-4-12 Group the first three terms.


%28x%2B2%29%5E2-4-12 Factor x%5E2%2B4x%2B4 to get %28x%2B2%29%5E2.


%28x%2B2%29%5E2-16 Combine like terms.


So after completing the square, x%5E2%2B4x-12 transforms to %28x%2B2%29%5E2-16. So x%5E2%2B4x-12=%28x%2B2%29%5E2-16.


So x%5E2%2B4x-12=0 is equivalent to %28x%2B2%29%5E2-16=0.


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%28x%2B2%29%5E2-16=0 Start with the given equation.


%28x%2B2%29%5E2=0%2B16Add 16 to both sides.


%28x%2B2%29%5E2=16 Combine like terms.


x%2B2=0%2B-sqrt%2816%29 Take the square root of both sides.


x%2B2=sqrt%2816%29 or x%2B2=-sqrt%2816%29 Break up the "plus/minus" to form two equations.


x%2B2=4 or x%2B2=-4 Take the square root of 16 to get 4.


x=-2%2B4 or x=-2-4 Subtract 2 from both sides.


x=2 or x=-6 Combine like terms.


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Answer:


So the solutions are x=2 or x=-6.