Answer:
[tex]\boxed{x_{1}=-3} \\ \\ \boxed{x_{2}=11}[/tex]
Explanation:
Step 1. Write [tex]x^2 - 8x - 33=0[/tex] in the form [tex]x^2+2ax+a^2=0[/tex]
[tex]2a=-8\quad :\quad a=-4[/tex]
Step 2. Add and subtract [tex](-4)^2[/tex] to the left side of the equation
[tex]x^2-8x-33+\left(-4\right)^2-\left(-4\right)^2=0 \\ \\ \\ But: \\ \\ x^2+2ax+a^2=\left(x+a\right)^2 \\ \\ x^2-8x+\left(-4\right)^2=\left(x-4\right)^2[/tex]
Step 3. Complete square
[tex]\left(x-4\right)^2-33-\left(-4\right)^2=0 \\ \\ \left(x-4\right)^2-49=0 \\ \\ (x-4)=\pm \sqrt{49} \\ \\ x-4=\pm 7 \\ \\ \boxed{x_{1}=-3} \\ \\ \boxed{x_{2}=11}[/tex]
