Question

question 2 of 10
find the solutions to the equation below.
check all that apply.
$x^2 - 25 = 0$

a. $x = 3$
b. $x = -3$
c. $x = -1$
d. $x = 5$
e. $x = 1$
f. $x = -5$

Explanation:

Step1: Solve the equation \(x^2 - 25 = 0\)

We can rewrite the equation as a difference of squares: \(x^2 - 5^2 = 0\). Using the formula \(a^2 - b^2=(a - b)(a + b)\), we get \((x - 5)(x + 5)=0\).

Step2: Find the roots

For a product of factors to be zero, at least one of the factors must be zero. So we set each factor equal to zero:

• If \(x - 5 = 0\), then \(x = 5\).
• If \(x + 5 = 0\), then \(x=-5\).

Answer:

D. \(x = 5\), F. \(x=-5\)