Question

What equation results from completing the square and then factoring?

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

Answer 1

`\boxed{ (x + 5)^2 = 40}`

Explanation:

`x^2 + 10x= 15`

`ax^2 +bx=-c`

Add
`((b)/(2) )^2` on both sides.

`((10)/(2) )^2 =5^2 =25`

`x^2 + 10x+25= 15+25`

`x^2 + 10x+25= 40`

Factor left side of the equation.

`(x + 5)^2 = 40`

Answer 2

B

Explanation:

Given

x² + 10x = 15

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = 15 + 25, that is

(x + 5)² = 40 → B