Question 316
We'll start from where you left off. If you look at the first part of the problem you will have {{{(x+(x+2))^2=2(x+4)}}}. Combine like terms to get {{{(2x+2)^2=2(x+4)}}}. Multiply it out to get {{{4x^2+8x+4=2x+8}}}.
Combine like terms again to get {{{4x^2+6x-4=0}}}. Factor the equation to get {{{2(2x^2+3x-2)=0}}} and then {{{2(2x-1)(x+2)=0}}}. Solve for x to get {{{x=1/2}}} or {{{x=-2}}}. Due to the original problem saying three consecutive even integers, we can eliminate {{{x=1/2}}}. So the final answer is -2, 0, 2.