Divide the coefficient of x by 2 then square the quotient.
Add the result to both sides of the equation.
[tex]x^2 + 8x = 33[/tex]
[tex]x^2 + 8x + (\frac{8}{2})^2 = 33 + (\frac{8}{2})^2[/tex]
[tex]x^2 + 8x + 4^2 = 33 + 4^2[/tex]
[tex]x^2 + 8x + 16 = 33 + 16[/tex]
[tex]x^2 + 8x + 16 = 49[/tex]
Factor the left-hand side.
[tex](x + 4)^2 = 49[/tex]
Square both sides.
[tex]x + 4 = \sqrt{49}[/tex]
Subtract both sides by 4.
[tex] x = -4[/tex][tex]± \sqrt{49}[/tex]
Simplify.
[tex] x = -4[/tex][tex]± 7[/tex]
So, x can either equal -4 + 7 or -4 - 7
So, the answer is {-11, 3}
NOTE: You're probably seeing a strange A in the equations. I tried to fix it, but I couldn't. Sorry about that.
