SOLUTION: Show that 2x^2-12x+23 is equal to 2(x+3)^2+5

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Question 252147: Show that 2x^2-12x+23 is equal to 2(x+3)^2+5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I think you made a typo. The problem should be "Show that 2x^2-12x+23 is equal to 2(x-3)^2+5"


2x%5E2-12x%2B23 Start with the given expression.


2%28x%5E2-6x%2B23%2F2%29 Factor out the x%5E2 coefficient 2. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -6 to get -3. In other words, %281%2F2%29%28-6%29=-3.


Now square -3 to get 9. In other words, %28-3%29%5E2=%28-3%29%28-3%29=9


2%28x%5E2-6x%2Bhighlight%289-9%29%2B23%2F2%29 Now add and subtract 9 inside the parenthesis. Make sure to place this after the "x" term. Notice how 9-9=0. So the expression is not changed.


2%28%28x%5E2-6x%2B9%29-9%2B23%2F2%29 Group the first three terms.


2%28%28x-3%29%5E2-9%2B23%2F2%29 Factor x%5E2-6x%2B9 to get %28x-3%29%5E2.


2%28%28x-3%29%5E2%2B5%2F2%29 Combine like terms.


2%28x-3%29%5E2%2B2%285%2F2%29 Distribute.


2%28x-3%29%5E2%2B5 Multiply.


So after completing the square, 2x%5E2-12x%2B23 transforms to 2%28x-3%29%5E2%2B5. So 2x%5E2-12x%2B23=2%28x-3%29%5E2%2B5 for all real values of 'x'.