Question

x² - 8x - 33=0
complete the square

Answer 1

Answer:

$\boxed{x_{1}=-3} \\ \\ \boxed{x_{2}=11}$

Explanation:

Step 1. Write $x^2 - 8x - 33=0$ in the form $x^2+2ax+a^2=0$

$2a=-8\quad :\quad a=-4$

Step 2. Add and subtract $(-4)^2$ to the left side of the equation

$x^2-8x-33+\left(-4\right)^2-\left(-4\right)^2=0 \\ \\ \\ But: \\ \\ x^2+2ax+a^2=\left(x+a\right)^2 \\ \\ x^2-8x+\left(-4\right)^2=\left(x-4\right)^2$

Step 3. Complete square

$\left(x-4\right)^2-33-\left(-4\right)^2=0 \\ \\ \left(x-4\right)^2-49=0 \\ \\ (x-4)=\pm \sqrt{49} \\ \\ x-4=\pm 7 \\ \\ \boxed{x_{1}=-3} \\ \\ \boxed{x_{2}=11}$