The first few steps in solving the quadratic equation 9x2 + 49x = 22 − 5x by completing the square are shown. 9x2 + 49x = 22 − 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 which is the best step to do next to solve the equation by completing the square? a: 9(x2 + 6x + 3) = 25 b: 9(x2 + 6x + 3) = 49 c: 9(x2 + 6x + 9) = 31 d: 9(x2 + 6x + 9) = 103

We are given a quadratic equation: .

We need to solve the quadratic equation by completing the square.

First step is adding 5x on both sides, we get

.

Then we need to factor out common factor 9.

We get

.

In order to complete the square, we need to find the square of the half of 6.

Half of the 6 is 3.

And square of 3 is 9.

So, we need to add 9 inside parenthesis and 9*9 = 81 on right side. We get

On simplifying this step, we get

.

We have been given a quadratic equation and we are asked to find next step to solve the equation by completing the square.

Let us solve our quadratic equation by completing the square method.

Upon factoring out 9 we will get,  

Since we know that we take square of half of the middle term. So our last term will be,

To hold this equation true we will add same number to both sides of equation. We will add 81 to right hand of our equation as 9 times 9 is 81.

So our next step will be,

Therefore, option D is the correct choice.

step-by-step explanation:

infinity is the answer