SOLUTION: Put the equation 5x^2-10x-2 in turning point form a(x-h)^2+k, by completing the square.

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Question 276999: Put the equation 5x^2-10x-2 in turning point form a(x-h)^2+k, by completing the square.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5x%5E2-10x-2 Start with the given expression.


5%28x%5E2-2x-2%2F5%29 Factor out the x%5E2 coefficient 5. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -2 to get -1. In other words, %281%2F2%29%28-2%29=-1.


Now square -1 to get 1. In other words, %28-1%29%5E2=%28-1%29%28-1%29=1


5%28x%5E2-2x%2Bhighlight%281-1%29-2%2F5%29 Now add and subtract 1 inside the parenthesis. Make sure to place this after the "x" term. Notice how 1-1=0. So the expression is not changed.


5%28%28x%5E2-2x%2B1%29-1-2%2F5%29 Group the first three terms.


5%28%28x-1%29%5E2-1-2%2F5%29 Factor x%5E2-2x%2B1 to get %28x-1%29%5E2.


5%28%28x-1%29%5E2-7%2F5%29 Combine like terms.


5%28x-1%29%5E2%2B5%28-7%2F5%29 Distribute.


5%28x-1%29%5E2-7 Multiply.


So after completing the square, 5x%5E2-10x-2 transforms to 5%28x-1%29%5E2-7. So 5x%5E2-10x-2=5%28x-1%29%5E2-7.