Solve u^2+190=0

$$u ^ { 2 } + 190 = 0$$

Solve for u

$$u=-\sqrt{190}i\approx -0-13.784048752i$$

$$u=\sqrt{190}i\approx 13.784048752i$$

Steps by Finding Square Root

Subtract 190 from both sides. Anything subtracted from zero gives its negation.

$$u^{2}=-190$$

The equation is now solved.

$$u=\sqrt{190}i u=-\sqrt{190}i$$

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.

$$u^{2}+190=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 190 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{0±\sqrt{0^{2}-4\times 190}}{2}$$

Square 0.

$$u=\frac{0±\sqrt{-4\times 190}}{2}$$

Multiply -4 times 190.

$$u=\frac{0±\sqrt{-760}}{2}$$

Take the square root of -760.

$$u=\frac{0±2\sqrt{190}i}{2}$$

Now solve the equation u=\frac{0±2\sqrt{190}i}{2} when ± is plus.

$$u=\sqrt{190}i$$

Now solve the equation u=\frac{0±2\sqrt{190}i}{2} when ± is minus.

$$u=-\sqrt{190}i$$

The equation is now solved.

$$u=\sqrt{190}i u=-\sqrt{190}i$$