(2x-5)^2=42

2 min read Jun 16, 2024

Solving the Equation: (2x-5)^2 = 42

This equation involves a squared term, which can be solved by following a few steps. Here's a breakdown of the solution:

1. Isolate the Squared Term

First, we need to get the term (2x-5)^2 by itself on one side of the equation. Since the equation is already in this form, we can move on to the next step.

2. Take the Square Root of Both Sides

To get rid of the square, we take the square root of both sides of the equation. Remember that taking the square root results in both a positive and a negative solution:

√[(2x-5)^2] = ±√42

This simplifies to:

2x-5 = ±√42

3. Solve for x

Now we have two separate equations to solve:

Equation 1: 2x-5 = √42 Equation 2: 2x-5 = -√42

Solving Equation 1:

Add 5 to both sides: 2x = √42 + 5
Divide both sides by 2: x = (√42 + 5)/2

Solving Equation 2:

Add 5 to both sides: 2x = -√42 + 5
Divide both sides by 2: x = (-√42 + 5)/2

4. The Solutions

Therefore, the solutions to the equation (2x-5)^2 = 42 are:

x = (√42 + 5)/2
x = (-√42 + 5)/2

These are the two values of x that satisfy the original equation.