Question

math test
write your answer in the comments!
\\(x + 3)^2 = 25\\
\\x = ?\\

Explanation:

Identify the given equation

We are given a quadratic equation in vertex form:

$$(x + 3)^2 = 25$$

Our goal is to solve for \(x\).

Apply the square root property

To isolate the term inside the parentheses, we take the square root of both sides of the equation. Remember that taking the square root of a positive number yields both a positive and a negative root:

$$x + 3 = \pm\sqrt{25}$$

$$x + 3 = \pm 5$$

Set up two separate linear equations

This gives us two distinct equations to solve:

1. \(x + 3 = 5\)
2. \(x + 3 = -5\)

Solve each equation for x

For the first equation:

$$x = 5 - 3$$

$$x = 2$$

For the second equation:

$$x = -5 - 3$$

$$x = -8$$

Thus, the solutions are \(x = 2\) or \(x = -8\).

Answer:

If \((x + 3)^2 = 25\), then \(x =\) <blank>\(2\)</blank> or <blank>\(-8\)</blank>.