Solve The Equation $x^2 - \frac{16}{25} = 0$.1. Isolate $x^2$: $\[x^2 = \frac{16}{25}\\]2. Apply The Square Root Property Of Equality: $\[\sqrt{x^2} = \pm \sqrt{\frac{16}{25}}\\]What Are The Solutions To The

Solving the Equation $x^2 - \frac{16}{25} = 0$

In this article, we will explore the process of solving a quadratic equation of the form $x^2 - \frac{16}{25} = 0$. This type of equation is a quadratic equation in its simplest form, where the variable $x$ is squared and then subtracted by a constant term. Our goal is to isolate the variable $x$ and find its solutions.

Step 1: Isolate $x^2$

The first step in solving the equation is to isolate the term $x^2$. To do this, we add $\frac{16}{25}$ to both sides of the equation:

$$x^2 - \frac{16}{25} = 0$$

$$x^2 = \frac{16}{25}$$

By adding $\frac{16}{25}$ to both sides, we have isolated the term $x^2$ and have simplified the equation.

Step 2: Apply the Square Root Property of Equality

Now that we have isolated $x^2$, we can apply the square root property of equality. This property states that if $x^2 = a$, then $x = \pm \sqrt{a}$. In our case, we have $x^2 = \frac{16}{25}$, so we can apply the square root property as follows:

$$\sqrt{x^2} = \pm \sqrt{\frac{16}{25}}$$

$$x = \pm \sqrt{\frac{16}{25}}$$

By applying the square root property, we have found the solutions to the equation.

Solutions to the Equation

Now that we have applied the square root property, we can simplify the solutions to the equation. We have:

$$x = \pm \sqrt{\frac{16}{25}}$$

To simplify the square root, we can find the square root of the numerator and the denominator separately:

$$x = \pm \frac{\sqrt{16}}{\sqrt{25}}$$

$$x = \pm \frac{4}{5}$$

Therefore, the solutions to the equation are $x = \frac{4}{5}$ and $x = -\frac{4}{5}$.

In this article, we have solved the quadratic equation $x^2 - \frac{16}{25} = 0$ using the square root property of equality. We first isolated the term $x^2$ by adding $\frac{16}{25}$ to both sides of the equation. Then, we applied the square root property to find the solutions to the equation. Finally, we simplified the solutions to find the final answers.

The final answer to the equation $x^2 - \frac{16}{25} = 0$ is:

$$x = \pm \frac{4}{5}$$

This means that the solutions to the equation are $x = \frac{4}{5}$ and $x = -\frac{4}{5}$.
Solving the Equation $x^2 - \frac{16}{25} = 0$: Q&A

In our previous article, we solved the quadratic equation $x^2 - \frac{16}{25} = 0$ using the square root property of equality. We isolated the term $x^2$ and then applied the square root property to find the solutions to the equation. In this article, we will answer some frequently asked questions about solving quadratic equations and provide additional examples.

Q: What is the square root property of equality?

A: The square root property of equality states that if $x^2 = a$, then $x = \pm \sqrt{a}$. This means that if we have an equation where the variable is squared, we can find the solutions by taking the square root of both sides of the equation.

Q: How do I isolate the term $x^2$ in a quadratic equation?

A: To isolate the term $x^2$, you need to add or subtract the same value from both sides of the equation. For example, if we have the equation $x^2 - \frac{16}{25} = 0$, we can add $\frac{16}{25}$ to both sides to isolate the term $x^2$.

Q: What if the equation has a coefficient in front of the $x^2$ term?

A: If the equation has a coefficient in front of the $x^2$ term, you need to factor out the coefficient before isolating the term $x^2$. For example, if we have the equation $2x^2 - \frac{16}{25} = 0$, we can factor out the coefficient 2 to get $2(x^2 - \frac{8}{25}) = 0$. Then, we can isolate the term $x^2$ by adding $\frac{8}{25}$ to both sides.

Q: Can I use the square root property of equality with negative numbers?

A: Yes, you can use the square root property of equality with negative numbers. However, you need to be careful when taking the square root of a negative number, as it will result in a complex number. For example, if we have the equation $x^2 + 4 = 0$, we can take the square root of both sides to get $x = \pm \sqrt{-4}$. This will result in a complex number, $x = \pm 2i$.

Q: What if the equation has a fraction in the $x^2$ term?

A: If the equation has a fraction in the $x^2$ term, you need to simplify the fraction before isolating the term $x^2$. For example, if we have the equation $x^2 - \frac{16}{25} = 0$, we can simplify the fraction by finding the greatest common divisor of the numerator and the denominator. In this case, the greatest common divisor is 1, so the fraction is already simplified.

Q: Can I use the square root property of equality with decimal numbers?

A: Yes, you can use the square root property of equality with decimal numbers. However, you need to be careful when taking the square root of a decimal number, as it may result in a non-integer value. For example, if we have the equation $x^2 - 0.64 = 0$, we can take the square root of both sides to get $x = \pm \sqrt{0.64}$. This will result in a non-integer value, $x = \pm 0.8$.

In this article, we have answered some frequently asked questions about solving quadratic equations and provided additional examples. We have also discussed how to isolate the term $x^2$ in a quadratic equation, how to handle coefficients and fractions in the $x^2$ term, and how to use the square root property of equality with negative numbers and decimal numbers.

The final answer to the equation $x^2 - \frac{16}{25} = 0$ is:

$$x = \pm \frac{4}{5}$$

This means that the solutions to the equation are $x = \frac{4}{5}$ and $x = -\frac{4}{5}$.