Solve x^2+5*+1=0

$${ x }^{ 2 } +5 \times +1=0$$

Solve for x (complex solution)

$$x=-\sqrt{5}i\approx -0-2.236067977i$$

$$x=\sqrt{5}i\approx 2.236067977i$$

Steps by Finding Square Root

Multiply 5 and 1 to get 5.

$$x^{2}+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-5$$

The equation is now solved.

$$x=\sqrt{5}i x=-\sqrt{5}i$$

Steps Using the Quadratic Formula

Multiply 5 and 1 to get 5.

$$x^{2}+5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5}}{2}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20}}{2}$$

Take the square root of -20.

$$x=\frac{0±2\sqrt{5}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{5}i}{2} when ± is plus.

$$x=\sqrt{5}i$$

Now solve the equation x=\frac{0±2\sqrt{5}i}{2} when ± is minus.

$$x=-\sqrt{5}i$$

The equation is now solved.

$$x=\sqrt{5}i x=-\sqrt{5}i$$