Let's solve the given equation step-by-step to find the number of real number solutions.
The equation we are given is:
[tex]\[ x^2 - 6 = 0 \][/tex]
Step 1: Move the constant term to the other side of the equation.
[tex]\[ x^2 = 6 \][/tex]
Step 2: Take the square root of both sides to solve for [tex]\( x \)[/tex].
[tex]\[ x = \pm \sqrt{6} \][/tex]
Step 3: Identify the solutions obtained.
[tex]\[ x = \sqrt{6} \quad \text{or} \quad x = -\sqrt{6} \][/tex]
Step 4: Count the number of distinct real solutions.
We have two solutions here: [tex]\( x = \sqrt{6} \)[/tex] and [tex]\( x = -\sqrt{6} \)[/tex].
Therefore, the number of real number solutions for the equation [tex]\( x^2 - 6 = 0 \)[/tex] is 2.
