Answer :
Sure, let's solve the equation [tex]\( x^2 = 169 \)[/tex].
Step-by-Step Solution:
1. Identify the Equation: We are given the equation [tex]\( x^2 = 169 \)[/tex].
2. Understand the Goal: We need to find the value(s) of [tex]\( x \)[/tex] that satisfy the equation.
3. Take the Square Root of Both Sides:
- To solve for [tex]\( x \)[/tex], we can take the square root of both sides of the equation.
- The square root of [tex]\( x^2 \)[/tex] is [tex]\( x \)[/tex], but remember that both positive and negative values will satisfy the equation because squaring either a positive or a negative number gives a positive result.
- So, [tex]\( x = \pm \sqrt{169} \)[/tex].
4. Calculate the Square Root of 169:
- The square root of 169 is 13.
- Hence, [tex]\( x = \pm 13 \)[/tex].
5. Solution: The solutions to the equation [tex]\( x^2 = 169 \)[/tex] are [tex]\( x = 13 \)[/tex] and [tex]\( x = -13 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{x = \pm 13} \][/tex]
So, the answer is option (C) [tex]\( x = \pm 13 \)[/tex].
Step-by-Step Solution:
1. Identify the Equation: We are given the equation [tex]\( x^2 = 169 \)[/tex].
2. Understand the Goal: We need to find the value(s) of [tex]\( x \)[/tex] that satisfy the equation.
3. Take the Square Root of Both Sides:
- To solve for [tex]\( x \)[/tex], we can take the square root of both sides of the equation.
- The square root of [tex]\( x^2 \)[/tex] is [tex]\( x \)[/tex], but remember that both positive and negative values will satisfy the equation because squaring either a positive or a negative number gives a positive result.
- So, [tex]\( x = \pm \sqrt{169} \)[/tex].
4. Calculate the Square Root of 169:
- The square root of 169 is 13.
- Hence, [tex]\( x = \pm 13 \)[/tex].
5. Solution: The solutions to the equation [tex]\( x^2 = 169 \)[/tex] are [tex]\( x = 13 \)[/tex] and [tex]\( x = -13 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{x = \pm 13} \][/tex]
So, the answer is option (C) [tex]\( x = \pm 13 \)[/tex].
