(x-8)^2=48

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x - 8)² = 48

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

1. Isolate the Squared Term

The left side of the equation already has the squared term isolated.

2. Take the Square Root of Both Sides

Remember that taking the square root introduces both positive and negative solutions.

√[(x - 8)²] = ±√48

3. Simplify the Square Root

√[(x - 8)²] = x - 8 √48 = √(16 * 3) = 4√3

Therefore, we have:

x - 8 = ±4√3

4. Solve for x

• Case 1: x - 8 = 4√3 x = 8 + 4√3

• Case 2: x - 8 = -4√3 x = 8 - 4√3

Solutions

The solutions to the equation (x - 8)² = 48 are:

• x = 8 + 4√3
• x = 8 - 4√3