(2x-3)^2=81

Jasonbradley

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Jun 16, 2024

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Solving the Equation (2x - 3)^2 = 81

This equation involves a squared term, so we'll need to use the square root property to solve it. Here's how:

1. Take the Square Root of Both Sides

The first step is to isolate the squared term by taking the square root of both sides of the equation. Remember that taking the square root results in both a positive and negative solution:

√[(2x - 3)^2] = ±√81

2. Simplify

Simplify both sides of the equation:

2x - 3 = ±9

3. Solve for x

Now we have two separate equations to solve:

• Equation 1: 2x - 3 = 9
• Equation 2: 2x - 3 = -9

Solving Equation 1:

1. Add 3 to both sides: 2x = 12
2. Divide both sides by 2: x = 6

Solving Equation 2:

1. Add 3 to both sides: 2x = -6
2. Divide both sides by 2: x = -3

Solutions:

Therefore, the solutions to the equation (2x - 3)^2 = 81 are x = 6 and x = -3.