Final answer:
To determine the missing value in the equation 8x² +48x+72=(2x+6)²5729, we first need to simplify the equation on the right side by expanding it. Then, we can set up a quadratic equation and solve for the missing value of x.
Step-by-step explanation:
To determine the missing value in the equation 8x² +48x+72=(2x+6)²5729, we first need to simplify the equation on the right side. (2x+6)²5729 can be expanded to 4x² + 24x + 36 = 5729. Then, we can set up the quadratic equation 8x² + 48x + 72 - 4x² - 24x - 36 = 0. Combining like terms, we get 4x² + 24x + 72 - 5729 = 0. Finally, we can solve this quadratic equation to find the missing value of x.