Question

What equation results from completing the square and then factoring? X^2+22x=31

A) (x+11)^2 = 152
B) (x+22)^2 = 152
C) (x+11)^2 = 53
D) (x+22)^2 = 53

Answer 1

Explanation:

Rewrite X^2+22x=31, leaving space after the "22x:"

X^2+22x = 31

The coefficient of x is 22. Take half of that, obtaining 11.

Square this result: 11^2 = 121.

Write in "+121 -121" after the x term:

X^2+22x + 121 - 121 = 31

Rewrite X^2+22x + 121 as

(x + 11)^2 -121 = 31

Add 121 to both sides:

(x + 11)^2 = 152

Take the square root of both sides:

x + 11 = ±√152 = ±2√38

Finally, x = -11 ±2√38.

This is "solution by completing the square"

Answer 2

Answer: OPTION A

Explanation:

We have this quadratic equation:
`x^2+22x=31`

In order to complete the square the first step is to pick the coefficient of the x term, divide it by 2 and square it. Then:

`((22)/(2))^2=11^2`

Now we must add 11² to both sides of the equation:

`x^2+22x+11^2=31+11^2`

Therefore, after complete the square and factor, we get:

`(x+11)^2=152`

This matches with the option A.