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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

Respuesta :

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:

c. [tex](x+1)^2=20[/tex]

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 [tex]x^2[/tex].

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

Given equation,

[tex]x^2+2x=19[/tex] -----(1)

Here, the coefficient of [tex]x^2[/tex] 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),

[tex]x^2+2x+1 = 19 + 1[/tex]

[tex](x+1)^2 = 20[/tex]    ( Because (a+b)² = a² + 2ab + b² )

⇒ Option C is  correct.

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