Sure! Let's solve the equation step by step.
1. Equation given:
[tex]\[
x^2 + 4 - 3 = 0
\][/tex]
2. Simplify the equation:
First, combine the constants on one side:
[tex]\[
x^2 + 4 - 3 = x^2 + 1 = 0
\][/tex]
So the simplified equation is:
[tex]\[
x^2 + 1 = 0
\][/tex]
3. Isolate [tex]\(x^2\)[/tex]:
Move the constant term to the other side of the equation:
[tex]\[
x^2 = -1
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], take the square root of both sides. Remember, taking the square root of a negative number involves imaginary numbers:
[tex]\[
x = \pm \sqrt{-1}
\][/tex]
5. Simplify the square root:
The square root of [tex]\(-1\)[/tex] is denoted by the imaginary unit [tex]\(i\)[/tex]:
[tex]\[
\sqrt{-1} = i
\][/tex]
Therefore, the solutions to the equation are:
[tex]\[
x = \pm i
\][/tex]
Which means:
[tex]\[
x = i \quad \text{or} \quad x = -i
\][/tex]
So, the complete set of solutions to the equation [tex]\(x^2 + 1 = 0\)[/tex] is:
[tex]\[
\boxed{x = -i, x = i}
\][/tex]
