(x+7) 2 −49=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x + 7)² - 49 = 0

This equation can be solved using a few different methods. Let's explore two common approaches:

Method 1: Factoring

1. Recognize the pattern: The equation is in the form of a difference of squares: (a² - b²) = (a + b)(a - b). In our case, a = (x + 7) and b = 7.

2. Factor the equation: (x + 7)² - 49 = (x + 7 + 7)(x + 7 - 7) = (x + 14)(x)

3. Set each factor to zero: (x + 14) = 0 or x = 0

4. Solve for x: x = -14 or x = 0

Therefore, the solutions to the equation (x + 7)² - 49 = 0 are x = -14 and x = 0.

Method 2: Expanding and Simplifying

1. Expand the square: (x + 7)² = x² + 14x + 49

2. Substitute and simplify: x² + 14x + 49 - 49 = 0 => x² + 14x = 0

3. Factor out x: x(x + 14) = 0

4. Set each factor to zero: x = 0 or x + 14 = 0

5. Solve for x: x = 0 or x = -14

Again, we arrive at the solutions x = -14 and x = 0.

Both methods lead to the same solutions. Choosing the method that best suits you depends on your preference and familiarity with different algebraic techniques.