Solve for all real values of x.

Question

x, squared, plus, 3, equals, 0
x
2
+3=
0

Solve the problem just like the example below
⬇️
Solve for all real values of x

x² - 16 = 0
+16. +16

x²=16

√x² = ± √16

x= ± 4

Solutions: x=4, x=-4

Answer 1

Let's solve the equation \( x^2 + 3 = 0 \) step by step.

Step 1: Start with the original equation.

\[ x^2 + 3 = 0 \]

Step 2: Isolate the \( x^2 \) term.

\[ x^2 = -3 \]

Step 3: Take the square root of both sides.

\[ \sqrt{x^2} = \pm \sqrt{-3} \]

Step 4: Since \( \sqrt{-3} \) involves the imaginary unit \( i \), we can express it as follows:

\[ x = \pm i\sqrt{3} \]

Conclusion:

The solutions are complex and not real. Therefore, there are no real values of \( x \).

Solutions: There are no real solutions for this equation. The solutions are \( x = i\sqrt{3} \) and \( x = -i\sqrt{3} \).