Question

Richie is solving the equation x^2 −12x = 28 by completing the square. What number should he add to both sides of the equation to complete the square? A) 6 B) 12 C) 36 D) 64

Answer 1

Given,

The equation is, x^2-12x=28.

Comapring the given equation with

`(a-b)^2=a^2-2ab+b^2`

On comapring it obtains that,

`\begin{gathered} a^2=x^2 \\ a=x\ldots\text{.}(1) \end{gathered}`

Similarly,

`\begin{gathered} -2ab=-12x \\ -2* x* b=-12x \\ b=(-12x)/(-2x) \\ b=6 \end{gathered}`

Now,

`b^2=6*6=36`

Hence, 36 is added to both sides to make the equation complete square.

Hence, option d is correct