Question

What number must you add to complete the square? x^2+10x=15

A) (x+5)^2=15
B) (x+5)^2=40
C) (x+10)^2=15
D) (x+10)^2=40

Answer 1

`(x+5)^2=40`

Explanation:

The number to be added is the square of half of the linear term coefficient. Such coefficient in our case is "10" (the number accompanying the variable x). Then, half of it is 10/2 = 5, and that number squared gives 25.

Therefore, the number to add on bothsides of the equality is 25, which leads to the following:

`x^2+10x+25=15+25\\x^2+10x+25=40\\x^2+5x+5x+25=40\\x(x+5)+5(x+5)=40\\\\(x+5)^2=40`

This matches answer B) of your choices.