(x-4)^2=20

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x - 4)² = 20

This article will guide you through the steps of solving the equation (x - 4)² = 20.

Understanding the Equation

The equation represents a quadratic equation in a slightly disguised form. Let's break it down:

• (x - 4)²: This is a squared term, meaning the expression (x - 4) is multiplied by itself.
• = 20: This indicates that the squared term is equal to 20.

Solving for x

To find the values of x that satisfy the equation, we follow these steps:

1. Take the square root of both sides: √(x - 4)² = ±√20

2. Simplify: x - 4 = ±√20

3. Isolate x: x = 4 ±√20

4. Simplify the radical: x = 4 ± 2√5

Therefore, the solutions to the equation (x - 4)² = 20 are:

• x = 4 + 2√5
• x = 4 - 2√5

Conclusion

We have successfully solved the equation (x - 4)² = 20 by utilizing the properties of square roots and basic algebraic manipulations. The solutions obtained are x = 4 + 2√5 and x = 4 - 2√5. Remember, whenever you take the square root of both sides of an equation, you must consider both the positive and negative solutions.