Short Answer 
The equation (x − 25)² = 36 can be solved by taking the square root of both sides, resulting in two cases: x − 25 = 6 and x − 25 = -6. After isolating x, the solutions are found to be 19 and 31.
Step 1: Understand the Equation
The equation we are dealing with is (x − 25)² = 36. This is a quadratic equation where we want to find the value of x. The goal is to isolate x by manipulating the equation using algebraic rules.
Step 2: Solve for x
To solve the equation, we first take the square root of both sides. This gives us two possibilities to consider:
- x ‚àí 25 = 6
- x ‚àí 25 = -6
Next, we will add 25 to both sides of each case, leading to two separate equations.
Step 3: Find the Solutions
After adding 25, we need to solve each case individually. This results in:
- x = 25 + 6 ‚Üí x = 31
- x = 25 – 6 ‚Üí x = 19
Thus, the solutions to the equation are 19 and 31.