EXPLANATION
Since we have the expression:
(x + a)^2 = b
And the quadratic expression:
[tex]x^2-7x\text{ = -9x - 2}[/tex]Adding +2 to both sides:
[tex]x^2-7x\text{ +2 = -9x}[/tex]Adding +9x to both sides:
[tex]x^2+2x+2=0[/tex]Now, rewriting the expression:
[tex]x^2+2x=-2[/tex]Now, completing the square of:
[tex]x^2+bx=c[/tex]We need to add b^2/4 to both sides:
[tex]\frac{2^2}{4}=\frac{4}{4}=1[/tex]Now, we get:
[tex]x^2+2x+1=-2+1[/tex]and get:
[tex](x+1)^2=-1[/tex]Therefore, we need to take square roots of the expression to get:
[tex]\sqrt{(x+1)^2}=\sqrt{-1}[/tex][tex]x+1=i[/tex]Isolating x:
[tex]x=-1\pm i[/tex]Therefore:
[tex]x^2+2x+2=[/tex][tex]=(-1+i)(-1-i)[/tex]