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

Answer:

Step-by-step 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

Step-by-step 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:

$(\frac{22}{2})^2=11^2$

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.