(x-9)2=64

2 min read Jun 17, 2024

Solving the Equation: (x-9)² = 64

This equation involves a squared term, which means we'll need to use the square root property to solve for x. Here's a step-by-step guide:

1. Isolate the Squared Term

The first step is to get the term (x-9)² by itself on one side of the equation. Since the equation is already in this form, we can move directly to the next step.

2. Apply the Square Root Property

The square root property states that if a² = b, then a = ±√b. Applying this to our equation, we get:

(x - 9) = ±√64

3. Simplify the Square Root

√64 simplifies to 8, so our equation becomes:

(x - 9) = ±8

4. Solve for x

Now we have two possible equations:

x - 9 = 8
x - 9 = -8

Solving for x in each equation:

x = 17
x = 1

Solution

Therefore, the solutions to the equation (x-9)² = 64 are x = 17 and x = 1.