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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 :

GinnyAnsweridn
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]
Hi1315idn

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 .

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