Question

what is the intermediate step in the form as a result of completing the square for the following equation

Answer 1

Answer:

The intermediate step in the form;

$(x+a)^2=b\text{ }$

is;

$\begin{gathered} (x+(-6))^2=8 \\ \\ \text{where;} \\ a=-6 \\ b=8 \end{gathered}$

Explanation:

Given the quadratic equation;

$x^2-12x+32=4$

solving by completing the square;

$\begin{gathered} x^2-12x+32=4 \\ x^2-12x+32-32=4-32 \\ x^2-12x=-28 \\ \text{completing the square;} \\ x^2-12x+6^2=-28+6^2 \\ x^2-12x+36=-28+36 \end{gathered}$

Factorizing;

$\begin{gathered} x^2-12x+36=-28+36 \\ (x-6)^2=8 \end{gathered}$

Therefore, the intermediate step in the form;

$(x+a)^2=b\text{ }$

is;

$\begin{gathered} (x+(-6))^2=8 \\ \\ \text{where;} \\ a=-6 \\ b=8 \end{gathered}$