Question

using the square root property to solve an equation
what is the first step in solving the equation $x^2 - \frac{16}{25} = 0$?
what is the second step in solving the equation?

Explanation:

First Step:

Step1: Isolate \( x^2 \)

To solve the equation \( x^2 - \frac{16}{25} = 0 \), the first step is to isolate the \( x^2 \) term. We do this by adding \( \frac{16}{25} \) to both sides of the equation.
$$x^2 - \frac{16}{25} + \frac{16}{25} = 0 + \frac{16}{25}$$
Simplifying, we get:
$$x^2 = \frac{16}{25}$$

Second Step:

Step1: Apply Square Root Property

Now that \( x^2 = \frac{16}{25} \), we use the square root property, which states that if \( x^2 = a \), then \( x = \pm\sqrt{a} \). Applying this property to our equation:
$$x = \pm\sqrt{\frac{16}{25}}$$

Step2: Simplify the Square Root

Simplify \( \sqrt{\frac{16}{25}} \). Since \( \sqrt{16} = 4 \) and \( \sqrt{25} = 5 \), we have:
$$x = \pm\frac{4}{5}$$

Answer:

s:
First step: Add \( \frac{16}{25} \) to both sides to get \( x^2 = \frac{16}{25} \).
Second step: Take the square root of both sides and simplify to get \( x = \pm\frac{4}{5} \).