Question

the first three steps for solving the quadratic equation by completing the square are shown. fill in the missing number in the last step.\\(9x^2 + 54x = 7\\)\\(9(x^2 + 6x) = 7\\)\\(9(x^2 + 6x + 9) = 7 + \square\\)

Explanation:

Step1: Factor out coefficient from left

$9x^2 + 54x = 7$ becomes $9(x^2 + 6x) = 7$

Step2: Complete the square inside parentheses

For $x^2+6x$, add $(\frac{6}{2})^2=9$. Multiply by 9 for balance: $9\times9=81$

Step3: Add the balanced value to right

$9(x^2 + 6x + 9) = 7 + 81$

Answer:

81