Question

If \(x^2 - 9 = 0\), what is the value of x?

• A. 3
• B. -3
• C. 3 or -3
• D. 9

Hint:

Remember that taking the square root of a positive number yields two solutions: one positive and one negative. This is a common point where errors are made.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a quadratic equation. We can solve it by isolating \(x^2\) and taking the square root of both sides.
Step 2: Detailed Explanation:
The given equation is a difference of squares: \(a^2 - b^2 = (a-b)(a+b)\).
\[ x^2 - 9 = 0 \] \[ x^2 - 3^2 = 0 \] \[ (x - 3)(x + 3) = 0 \] This equation is true if either factor is zero:
\(x - 3 = 0 \implies x = 3\)
or
\(x + 3 = 0 \implies x = -3\)
Alternatively, we can isolate \(x^2\):
\[ x^2 = 9 \] Taking the square root of both sides, we must consider both the positive and negative roots:
\[ x = \pm\sqrt{9} \] \[ x = 3 \text{ or } x = -3 \] Step 3: Final Answer:
The possible values for \(x\) are 3 and -3. This corresponds to option (C).