Question

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

Answer 1

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}`

Step-by-step 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}`