Solve 0=1+u_1^2

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

Solve for u_1

$$u_{1}=-i$$

$$u_{1}=i$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

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

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

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

The equation is now solved.

$$u_{1}=i u_{1}=-i$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

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

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.

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

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}.

$$u_{1}=\frac{0±\sqrt{0^{2}-4}}{2}$$

Square 0.

$$u_{1}=\frac{0±\sqrt{-4}}{2}$$

Take the square root of -4.

$$u_{1}=\frac{0±2i}{2}$$

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

$$u_{1}=i$$

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

$$u_{1}=-i$$

The equation is now solved.

$$u_{1}=i u_{1}=-i$$