Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Question 5 of 10

Find the solutions to the equation below. Check all that apply.

[tex]\[ x^2 - 9 = 0 \][/tex]

A. [tex]\( x = -3 \)[/tex]
B. [tex]\( x = 2 \)[/tex]
C. [tex]\( x = 3 \)[/tex]
D. [tex]\( x = -1 \)[/tex]
E. [tex]\( x = 1 \)[/tex]
F. [tex]\( x = -2 \)[/tex]

Sagot :

GinnyAnswer
To find the solutions to the equation [tex]\( x^2 - 9 = 0 \)[/tex], we need to solve for [tex]\( x \)[/tex].

1. The given equation is:
[tex]\[ x^2 - 9 = 0 \][/tex]

2. We can rewrite this equation to find the values of [tex]\( x \)[/tex]:
[tex]\[ x^2 - 9 = 0 \implies x^2 = 9 \][/tex]

3. To isolate [tex]\( x \)[/tex], we take the square root of both sides of the equation. Remember that taking the square root of a number yields both a positive and a negative solution:
[tex]\[ x = \sqrt{9} \quad \text{and} \quad x = -\sqrt{9} \][/tex]

4. Calculate the square roots:
[tex]\[ \sqrt{9} = 3 \quad \text{and} \quad -\sqrt{9} = -3 \][/tex]

5. Therefore, the solutions to the equation [tex]\( x^2 - 9 = 0 \)[/tex] are:
[tex]\[ x = 3 \quad \text{and} \quad x = -3 \][/tex]

Now, let's check which of the provided options are solutions:

- A. [tex]\( x = -3 \)[/tex] is a solution.
- B. [tex]\( x = 2 \)[/tex] is not a solution.
- C. [tex]\( x = 3 \)[/tex] is a solution.
- D. [tex]\( x = -1 \)[/tex] is not a solution.
- E. [tex]\( x = 1 \)[/tex] is not a solution.
- F. [tex]\( x = -2 \)[/tex] is not a solution.

So, the correct answers are:

A. [tex]\( x = -3 \)[/tex]

C. [tex]\( x = 3 \)[/tex]
Hi1315

Answer:

A.  x = -3

C.  x = 3  

Step-by-step explanation:

To find the solutions to the equation  x² - 9 = 0 :

Add 9 to both sides:

[tex]\sf x^2 - 9 + 9 = 0 + 9 \\\\ x^2 = 9[/tex]

Take the square root of both sides:

[tex]\sf x = \pm \sqrt{9}\\\\ \pm 3[/tex]

So, the solutions are  x = 3  and  x = -3 .

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.