Answer :
- Take the square root of both sides of the equation: $x = \pm \sqrt{9}$.
- Simplify the square root: $x = \pm 3$.
- Identify the solutions from the options.
- The solutions are $3$ and $-3$, so the answer is $\boxed{3, -3}$.
### Explanation
1. Understanding the Problem
We are given the equation $x^2 = 9$ and asked to find all solutions from the given options. This is a quadratic equation, and we can solve it by taking the square root of both sides.
2. Taking the Square Root
Taking the square root of both sides of the equation $x^2 = 9$, we get $x = \pm \sqrt{9}$.
3. Simplifying
Simplifying the square root, we have $x = \pm 3$. This means $x = 3$ or $x = -3$.
4. Checking the Options
Now we check the given options to see which ones match our solutions. Option C is 3, and option D is -3. Therefore, the solutions are 3 and -3.
5. Final Answer
The solutions to the equation $x^2 = 9$ are $x = 3$ and $x = -3$.
### Examples
Understanding quadratic equations like $x^2 = 9$ is crucial in many real-world applications. For example, if you're designing a square garden with an area of 9 square meters, you need to solve this equation to find the length of each side. Similarly, in physics, this type of equation can appear when calculating distances or velocities in scenarios involving constant acceleration. Knowing how to solve these equations helps in practical design and analytical problem-solving.
- Simplify the square root: $x = \pm 3$.
- Identify the solutions from the options.
- The solutions are $3$ and $-3$, so the answer is $\boxed{3, -3}$.
### Explanation
1. Understanding the Problem
We are given the equation $x^2 = 9$ and asked to find all solutions from the given options. This is a quadratic equation, and we can solve it by taking the square root of both sides.
2. Taking the Square Root
Taking the square root of both sides of the equation $x^2 = 9$, we get $x = \pm \sqrt{9}$.
3. Simplifying
Simplifying the square root, we have $x = \pm 3$. This means $x = 3$ or $x = -3$.
4. Checking the Options
Now we check the given options to see which ones match our solutions. Option C is 3, and option D is -3. Therefore, the solutions are 3 and -3.
5. Final Answer
The solutions to the equation $x^2 = 9$ are $x = 3$ and $x = -3$.
### Examples
Understanding quadratic equations like $x^2 = 9$ is crucial in many real-world applications. For example, if you're designing a square garden with an area of 9 square meters, you need to solve this equation to find the length of each side. Similarly, in physics, this type of equation can appear when calculating distances or velocities in scenarios involving constant acceleration. Knowing how to solve these equations helps in practical design and analytical problem-solving.
