Question

Which equation is equivalent to x2 + 36x= 88?

Answer 1

We must complete the square in order to solve the problem.

Now, the first step is to realize that if we have factor a quadratic (x+a)^2

`(x+a)^2=x^2+2ax+a^2^{}`

which, in our case, implies

`2ax=36x`
`\therefore a=18`

Therefore, we add 18^2 to both sides of the equation such that

`x^2+36x\textcolor{#FF7968}{+18^2}=(x+18)^2`

this gives

`x^2+36x+18^2=88+18^2`
`\textcolor{#FF7968}{\Rightarrow(x+18)^2=412}`

which is choice c from the options.