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

Question 252147: Show that 2x^2-12x+23 is equal to 2(x+3)^2+5
Answer by jim_thompson5910(35256) (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"

Start with the given expression.

Factor out the coefficient . This step is very important: the coefficient must be equal to 1.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

Distribute.

Multiply.

So after completing the square, transforms to . So for all real values of 'x'.

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