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1. x^{2} + 4 = 0

   Start from the equation as given.

2. a = 1,\quad b = 0,\quad c = 4

   Read off the coefficients of the standard form ax² + bx + c = 0.

3. \Delta = b^2 - 4ac = (0)^2 - 4(1)(4) = -16

   It does not factor nicely, so use the discriminant Δ = b² − 4ac.

4. x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{0 \pm \sqrt{-16}}{2}

   Δ < 0, so the roots are a complex-conjugate pair. Substitute into the quadratic formula.

5. x = 2 i \quad\text{or}\quad x = - 2 i

   Simplify each root.