Question

Which of the following correctly completes the square for the equation below?

Answer 1

Answer:

c. $(x+1)^2=20$

Step-by-step explanation:

Since, for getting a perfect square on the left side of a quadratic equation we follow the following steps,

Step 1 : Make 1 as the coefficient of $x^2$.

Step 2 : Add both side the square of a number which is half of the x's coefficient.

Given equation,

$x^2+2x=19$ -----(1)

Here, the coefficient of $x^2$ is already one.

And, the middle term is 2,

Half of 2 is 1

Also, 1² = 1

Thus, add 1 on both sides of equation (1),

$x^2+2x+1 = 19 + 1$

$(x+1)^2 = 20$    ( Because (a+b)² = a² + 2ab + b² )

⇒ Option C is  correct.

Answer 2

The answer is :

c. (x+1)²=20

To check:
(x+1)²=20                          (a+b)²=a²+2ab+b²
x²+2x+1=20
x²+2x=20-1
x²+2x=19