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

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"

OPTION A

Step-by-step explanation:

We have this quadratic equation:

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:

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

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

This matches with the option A.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2

step-by-step explanation:

107 units