SOLUTION: 1.)how do you complete the square of f(x)=x^2+4x+2 to the right hand side 2.)how do you complete the square of f(x)=-2x^2+6x+2 to the right handside

Algebra ->  Equations -> SOLUTION: 1.)how do you complete the square of f(x)=x^2+4x+2 to the right hand side 2.)how do you complete the square of f(x)=-2x^2+6x+2 to the right handside      Log On


   

Question 815078: 1.)how do you complete the square of f(x)=x^2+4x+2 to the right hand side
2.)how do you complete the square of f(x)=-2x^2+6x+2 to the right handside
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
I am giving help on your SECOND question because it requires more thorough skill than the FIRST question.

Factorize a -2 on the right side expression!
-2%28x%5E2-3x-1%29
NOW you are ready to complete the square, as long as you can identify the needed square term. Focus on the trinomial factor of x%5E2-3x-1;
The missing square term is highlight%28%28-3%2F2%29%5E2=9%2F4%29, and THAT is the term you both add and subtract INSIDE the parentheses.

f%28x%29=-2%28x%5E2-3x-1+%2B9%2F4+-9%2F4%29
f%28x%29=-2%28x%5E2-3x%2B9%2F4+-1-9%2F4%29
f%28x%29=-2%28%28x%5E2-3x%2B9%2F4%29-1-9%2F4%29
The grouping added is to emphasise,
f%28x%29=-2%28%28x-3%2F2%29%5E2-4%2F4-9%2F4%29
f%28x%29=-2%28%28x-3%2F2%29%5E2-13%2F4%29
And now perform the remultiplication to reverse the previous factorization.
highlight%28f%28x%29=-2%28x-3%2F2%29%5E2-13%2F2%29

Further, you might want to show 13%2F2 as 6%261%2F2