Solve using the square root method:
(
w
−
5
)
2
=
0
 

Enter each solution in the box below as a reduced fraction or integer. If there is more than 1 solution, separate the values with a comma (example: -3, 2).

The solution set for  
w
  is { 
 }  

To solve the equation \((w - 5)^2 = 0\) using the square root method, follow these steps:

1. **Take the square root of both sides**:
   \[
   \sqrt{(w - 5)^2} = \sqrt{0}
   \]
   This simplifies to:
   \[
   w - 5 = 0
   \]

2. **Solve for \(w\)**:
   \[
   w = 5
   \]

Since the square of a number is zero only when the number itself is zero, there is only one solution.

**The solution set for \(w\) is { 5 }**.

Would you like details or have any questions?

Here are 5 related questions to explore:
1. How do you solve quadratic equations using the square root method?
2. What is the difference between solving a quadratic equation by factoring and by using the square root method?
3. Can a quadratic equation have more than one solution when using the square root method?
4. What happens if there is a non-zero constant on the right side of the equation \((w - 5)^2 = 0\)?
5. How would you solve \((w - 7)^2 = 25\) using the square root method?

**Tip:** When dealing with equations like \((x - a)^2 = b\), remember to take the square root of both sides and consider both the positive and negative square roots of \(b\).

Solve using the square root method: (w − 5)^2 = 0. Enter each solution in the box below as a reduced fraction or integer. If there is more than 1 solution, separate the values with a comma (example: -3, 2). The solution set for w is { }

Discover how to solve the quadratic equation (w - 5)^2 = 0 using the square root method. This step-by-step guide explains key algebraic concepts, the square root method, and related theorems. Perfect for students in Grades 7-9 looking to strengthen their understanding of quadratic equations.

Math Problem Statement

Solve using the square root method: ( w − 5 ) 2

Solution

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