What are the solutions of the equation \(x^2 - 4 = 0\)?

What are the solutions of the equation \(x^2 - 4 = 0\)?

• A. \(x = 2\) and \(x = -2\)
• B. \(x = 4\) and \(x = -4\)
• C. \(x = 0\)
• D. \(x = 1\) and \(x = -1\)

Answer: (A)

To solve the equation \(x^2 - 4 = 0\), we start by recognizing that it can be factored. The expression \(x^2 - 4\) is a difference of squares, which can be factored into \((x - 2)(x + 2) = 0\). Setting each factor equal to zero gives us the following two equations: 1. \(x - 2 = 0\) which simplifies to \(x = 2\) 2. \(x + 2 = 0\) which simplifies to \(x = -2\) Thus, the solutions to the equation are \(x = 2\) and \(x = -2\). These solutions are correct as substituting them back into the original equation verifies that they satisfy the equation \(x^2 - 4 = 0\): - For \(x = 2\): \[ 2^2 - 4 = 4 - 4 = 0 \] - For \(x = -2\): \[ (-2)^2 - 4 = 4 - 4 = 0 \] Both values

To solve the equation (x^2 - 4 = 0), we start by recognizing that it can be factored. The expression (x^2 - 4) is a difference of squares, which can be factored into ((x - 2)(x + 2) = 0).

Setting each factor equal to zero gives us the following two equations:

1. (x - 2 = 0) which simplifies to (x = 2)

2. (x + 2 = 0) which simplifies to (x = -2)

Thus, the solutions to the equation are (x = 2) and (x = -2).

These solutions are correct as substituting them back into the original equation verifies that they satisfy the equation (x^2 - 4 = 0):

• For (x = 2):

[

2^2 - 4 = 4 - 4 = 0

]

• For (x = -2):

[

(-2)^2 - 4 = 4 - 4 = 0

]

Both values