the first few steps in solving the quadratic equation 9x² + 49x = 22 - 5x by completing the square are…

Explanation:

Step1: Recall the formula for completing the square

For the expression $x^{2}+bx$, to complete the square we add $\left(\frac{b}{2}\right)^{2}$. Here $b = 6$, so we add $\left(\frac{6}{2}\right)^{2}=9$ inside the parentheses. The left - hand side of the equation $9(x^{2}+6x)=22$ becomes $9(x^{2}+6x + 9)$ after adding 9 inside the parentheses.

Step2: Adjust the right - hand side

Since we added 9 inside the parentheses and the entire expression is multiplied by 9, we added $9\times9 = 81$ to the left - hand side. So we must add 81 to the right - hand side as well. The right - hand side $22$ becomes $22+81=103$. So the equation becomes $9(x^{2}+6x + 9)=103$.

Answer:

$9(x^{2}+6x + 9)=103$