I'm struggling . is appreciated , you !

x^2 + 4x + 1 = 10

x^2 + 4x + 1 + 3 = 10 + 3

x^2 + 4x + 4 = 13

(x + 2)^2 = 13

Answer

A.

(x + 2)^2 = 13

It's about matching patterns.

The square of the binomial (x+a) is

... (x+a)² = x² +2ax +a²

The first two terms of this match the first two terms of the left side of your equation if a=2. When we complete the square, your equation will look like

... (x+2)² = (something)

When that is written in expanded form, it is

... x² +2·2x +2² = (something)

... x² +4x +4 = (something)

Right now, your equation has a constant term of 1 on the left. In the above pattern, we see that we need to have a constant term of 4 on the left. To get there, we need to add 3 to the equation.

... x² +4x +1 +3 = 10 +3 . . . . . we have added 3 to both sides

... x² +4x +4 = 13 . . . . . . . . . . simplified

... (x +2)² = 13 . . . . . . . . . . . . . the left side written as a square

The appropriate answer choice is

... A (x+2)² = 13

step-by-step explanation: