(x-5)^2=4

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x-5)^2 = 4

This article will guide you through the steps of solving the equation (x-5)^2 = 4. We'll break down the process and explain each step clearly.

Understanding the Equation

The equation (x-5)^2 = 4 represents a quadratic equation. This means that the highest power of the variable 'x' is 2. Let's analyze what this equation means:

• (x-5): This represents a binomial expression.
• ^2: This means that the entire binomial (x-5) is squared, which means it's multiplied by itself.
• =4: This indicates that the result of squaring the binomial is equal to 4.

Solving for x

To find the value(s) of 'x' that satisfy this equation, we need to follow these steps:

1. Take the square root of both sides: This removes the square from the left side of the equation. Remember that taking the square root can result in both a positive and a negative solution.

   √((x-5)^2) = ±√4

2. Simplify: The square root of a squared term is simply the term itself.

   x-5 = ±2

3. Isolate x: To get 'x' by itself, add 5 to both sides of the equation.

   x = 5 ± 2

4. Calculate the solutions: This gives us two possible solutions:

   • x = 5 + 2 = 7
   • x = 5 - 2 = 3

Conclusion

Therefore, the solutions to the equation (x-5)^2 = 4 are x = 7 and x = 3.

This method can be applied to solve similar quadratic equations that are written in the form (x-a)^2 = b, where 'a' and 'b' are constants.