Let's solve the equation [tex]\( x^2 + 10 = 9 \)[/tex] step by step.
1. First, isolate the [tex]\( x^2 \)[/tex] term by subtracting 10 from both sides of the equation.
[tex]\[
x^2 + 10 - 10 = 9 - 10
\][/tex]
This simplifies to:
[tex]\[
x^2 = -1
\][/tex]
2. Next, we take the square root of both sides to solve for [tex]\( x \)[/tex].
[tex]\[
x = \pm \sqrt{-1}
\][/tex]
3. The square root of [tex]\(-1\)[/tex] is not a real number. In the real number system, the square root of a negative number does not exist. Therefore, we say there are no real number solutions to this equation.
Thus, the equation [tex]\( x^2 + 10 = 9 \)[/tex] has no real number solutions.
