Answer: x = 8, x = -2
Explanation:
(x - 3)² = 25
Step 1: Take the square root on each side of the equation.
(x - 3)² = 25
√(x - 3)² = ±√25
Step 2: After taking the square root on each side of the equation, this allows you to solve for x.
x - 3 = ±5
Solution 1
x - 3 = 5
x = 5 + 3
x = 8
Solution 2
x - 3 = - 5
x = -5 + 3
x = -2
Another way to solve this problem is to multiply (x - 3)² using the FOIL methods (first, outer, inner, last) and then set it equal to 25.
(x - 3) (x - 3) = 25
x² - 3x - 3x + 9 = 25
The next step is to add like terms. After adding like terms, solve for x.
x² - 3x - 3x + 9 = 25
x² - 6x + 9 - 25 = 25 - 25
x² - 6x - 16 = 0
Last step is to factor x² - 6x - 16 = 0 so you can solve for the two solutions.
(x - 8) (x + 2) = 0
Solution 1
x - 8 = 0
x = 8
Solution 2
x + 2 = 0
x = -2