Solve for x in the equation x^2 - 4 = 0.

₹0.0

Question: Solve for x in the equation x^2 - 4 = 0.

Options:

Correct Answer: x = 2, -2

Solution:

Factoring gives (x - 2)(x + 2) = 0. Thus, the solutions are x = 2 and x = -2.

Solve for x in the equation x^2 - 4 = 0.

Solve for x in the equation x^2 - 4 = 0.

Step 1: Start with the equation x^2 - 4 = 0.
Step 2: Recognize that x^2 - 4 is a difference of squares, which can be factored.
Step 3: Factor the equation into (x - 2)(x + 2) = 0.
Step 4: Set each factor equal to zero: x - 2 = 0 and x + 2 = 0.
Step 5: Solve the first equation x - 2 = 0 by adding 2 to both sides, giving x = 2.
Step 6: Solve the second equation x + 2 = 0 by subtracting 2 from both sides, giving x = -2.
Step 7: The solutions are x = 2 and x = -2.

Quadratic Equations – The question tests the ability to solve a simple quadratic equation using factoring.
Factoring – The solution requires knowledge of how to factor a quadratic expression.
Zero Product Property – The question tests understanding of the zero product property, which states that if the product of two factors is zero, at least one of the factors must be zero.