Question

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

x^2+2x=19
a. (x+2)^2=20
b. (x+1)^2=23
c. (x+1)^2=20
d. (x+2)^2=23

Answer 1

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

Answer 2

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

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.