Solve x^2+5.2+1=0

$${ x }^{ 2 } +5.2+1=0$$

Solve for x (complex solution)

$$x=-\frac{i\sqrt{155}}{5}\approx -0-2.48997992i$$

$$x=\frac{i\sqrt{155}}{5}\approx 2.48997992i$$

Steps by Finding Square Root

Add 5.2 and 1 to get 6.2.

$$x^{2}+6.2=0$$

Subtract 6.2 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-6.2$$

The equation is now solved.

$$x=\frac{\sqrt{155}i}{5} x=-\frac{\sqrt{155}i}{5}$$

Steps Using the Quadratic Formula

Add 5.2 and 1 to get 6.2.

$$x^{2}+6.2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 6.2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6.2}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6.2}}{2}$$

Multiply -4 times 6.2.

$$x=\frac{0±\sqrt{-24.8}}{2}$$

Take the square root of -24.8.

$$x=\frac{0±\frac{2\sqrt{155}i}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{155}i}{5}}{2} when ± is plus.

$$x=\frac{\sqrt{155}i}{5}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{155}i}{5}}{2} when ± is minus.

$$x=-\frac{\sqrt{155}i}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{155}i}{5} x=-\frac{\sqrt{155}i}{5}$$