Final answer:
The missing number in the equation (9 + )² = 25 can be either -4 or -14.
Step-by-step explanation:
The missing number can be found by rearranging the equation to isolate the unknown. Start by subtracting 25 from both sides:
(9 + )² - 25 = 0
Simplify the left side of the equation by expanding the square:
81 + 18() + ()² - 25 = 0
Combine like terms:
()² + 18() + 56 = 0
This equation is in the form of a quadratic equation. To solve for the missing number, we can use the quadratic formula:
() = [-18 ± √(18² - 4 * 1 * 56)] / 2
Using the formula, we find two possible solutions for the missing number:
() = [-18 ± √(324 - 224)] / 2
() = [-18 ± √100] / 2
() = [-18 ± 10] / 2
The two possible solutions are:
() = (-18 + 10) / 2 = -4
() = (-18 - 10) / 2 = -14
Therefore, the missing number in the equation (9 + )² = 25 can be either -4 or -14.
Learn more about Finding the missing number in an equation