Solve x_1^2+1=0

$$x _ { 1 } ^ { 2 } + 1 = 0$$

Solve for x_1

$$x_{1}=-i$$

$$x_{1}=i$$

Steps by Finding Square Root

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$x_{1}^{2}=-1$$

The equation is now solved.

$$x_{1}=i x_{1}=-i$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x_{1}^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x_{1}=\frac{0±\sqrt{0^{2}-4}}{2}$$

Square 0.

$$x_{1}=\frac{0±\sqrt{-4}}{2}$$

Take the square root of -4.

$$x_{1}=\frac{0±2i}{2}$$

Now solve the equation x_{1}=\frac{0±2i}{2} when ± is plus.

$$x_{1}=i$$

Now solve the equation x_{1}=\frac{0±2i}{2} when ± is minus.

$$x_{1}=-i$$

The equation is now solved.

$$x_{1}=i x_{1}=-i$$