Solve x^2+2pi=1

$$x ^ { 2 } + 2 \pi = 1$$

Solve for x (complex solution)

$$x=-i\sqrt{2\pi -1}\approx -0-2.298518068i$$

$$x=i\sqrt{2\pi -1}\approx 2.298518068i$$

Steps by Finding Square Root

Subtract 2\pi from both sides.

$$x^{2}=1-2\pi$$

The equation is now solved.

$$x=i\sqrt{2\pi -1} x=-i\sqrt{2\pi -1}$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$x^{2}+2\pi -1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(2\pi -1\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(2\pi -1\right)}}{2}$$

Multiply -4 times 2\pi -1.

$$x=\frac{0±\sqrt{4-8\pi }}{2}$$

Take the square root of -8\pi +4.

$$x=\frac{0±2i\sqrt{-\left(1-2\pi \right)}}{2}$$

Now solve the equation x=\frac{0±2i\sqrt{-\left(1-2\pi \right)}}{2} when ± is plus.

$$x=i\sqrt{2\pi -1}$$

Now solve the equation x=\frac{0±2i\sqrt{-\left(1-2\pi \right)}}{2} when ± is minus.

$$x=-i\sqrt{2\pi -1}$$

The equation is now solved.

$$x=i\sqrt{2\pi -1} x=-i\sqrt{2\pi -1}$$