(x-1)^2=4 Square Root Method

Jasonbradley

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Jun 17, 2024

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Solving Equations Using the Square Root Method: (x-1)^2 = 4

The square root method is a useful technique for solving quadratic equations that are in a specific form. This method relies on the concept of inverse operations to isolate the variable.

Here's how to solve the equation (x-1)^2 = 4 using the square root method:

Steps:

1. Isolate the squared term: The equation is already in the desired form.

2. Take the square root of both sides: This eliminates the square on the left side. Remember to consider both the positive and negative square roots:

   √[(x-1)^2] = ±√4
   

3. Simplify:

   x - 1 = ±2
   

4. Solve for x:

   • For the positive root:

     x - 1 = 2
     x = 2 + 1
     x = 3
     

   • For the negative root:

     x - 1 = -2
     x = -2 + 1
     x = -1
     

Solution:

Therefore, the solutions to the equation (x-1)^2 = 4 are x = 3 and x = -1.

Important Notes:

• Always remember to consider both the positive and negative square roots.
• The square root method is most effective when the quadratic equation is in the form (ax + b)^2 = c.

By following these steps, you can easily solve quadratic equations using the square root method.