Solve 58+x^2=3

$$58+ { x }^{ 2 } =3$$

Solve for x (complex solution)

$$x=-\sqrt{55}i\approx -0-7.416198487i$$

$$x=\sqrt{55}i\approx 7.416198487i$$

Steps by Finding Square Root

Subtract 58 from both sides.

$$x^{2}=3-58$$

Subtract 58 from 3 to get -55.

$$x^{2}=-55$$

The equation is now solved.

$$x=\sqrt{55}i x=-\sqrt{55}i$$

Steps Using the Quadratic Formula

Subtract 3 from both sides.

$$58+x^{2}-3=0$$

Subtract 3 from 58 to get 55.

$$55+x^{2}=0$$

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.

$$x^{2}+55=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 55 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 55}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 55}}{2}$$

Multiply -4 times 55.

$$x=\frac{0±\sqrt{-220}}{2}$$

Take the square root of -220.

$$x=\frac{0±2\sqrt{55}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{55}i}{2} when ± is plus.

$$x=\sqrt{55}i$$

Now solve the equation x=\frac{0±2\sqrt{55}i}{2} when ± is minus.

$$x=-\sqrt{55}i$$

The equation is now solved.

$$x=\sqrt{55}i x=-\sqrt{55}i$$