(x-4)2=16 Extracting Square Roots

Jasonbradley

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Jun 17, 2024

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Solving (x - 4)² = 16 by Extracting Square Roots

This equation represents a quadratic equation, but we can solve it using a simple method: extracting square roots. This technique allows us to isolate the variable by eliminating the square term. Here's how:

1. Isolate the squared term:

The equation already has the squared term isolated on the left side:

(x - 4)² = 16

2. Take the square root of both sides:

Remember that when taking the square root, we need to consider both positive and negative solutions.

√(x - 4)² = ±√16

3. Simplify:

This gives us:

x - 4 = ±4

4. Solve for x:

Now we have two possible solutions:

• Case 1: x - 4 = 4 Adding 4 to both sides, we get: x = 8

• Case 2: x - 4 = -4 Adding 4 to both sides, we get: x = 0

Therefore, the solutions to the equation (x - 4)² = 16 are x = 8 and x = 0.

Key Points:

• Extracting square roots is a useful method for solving quadratic equations that can be easily manipulated to isolate the squared term.
• Always remember to consider both positive and negative square roots when solving equations using this method.
• This method can be extended to solve equations with different constants on the right side of the equation.