Answer:
2(x + 3)^2 - 22
Step-by-step explanation:
2x^2 + 12x - 4
Start by making your "a" value equal to 1 by factoring the 2 from the first 2 terms in the standard form equation.
2(x^2 + 6x) - 4
Complete the square by using the formula (b/2)^2. Identify your "b" value, which is 6. Now you can complete the square.
((6)/2)^2 = 9
After completing the square, add 9 inside the parentheses and subtract 9 outside the parentheses. Since the 9 inside the parentheses is also being multiplied by 2, multiply the subtracted 9 by 2 as well.
2(x^2 + 6x + 9) - 4 - 9(2)
Factor the terms inside the parentheses by using the product/sum factoring method. This is where you find two of the same terms that multiply to "c" (9) and add to "b" (6).
In this case, positive 3 multiplies to 9 and adds to 6, so we will use the factors (x + 3)(x + 3), which is the same as (x + 3)^2.
2(x + 3)^2 - 4 - 9(2)
To finish off the problem, combine the like terms outside of the parentheses by multiplying 9 times 2 first and then subtracting -4 by 9(2).
[tex]\boxed{2(x + 3)^2 - 22 }[/tex]
