Solve pipi/4x^2+1=0

$$\pi \frac { \pi } { 4 } x ^ { 2 } + 1 = 0$$

Solve for x (complex solution)

$$x=\frac{-2i}{\pi }\approx -0.636619772i$$

$$x=\frac{2i}{\pi }\approx 0.636619772i$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$\pi \pi x^{2}+4=0$$

Multiply \pi and \pi to get \pi ^{2}.

$$\pi ^{2}x^{2}+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$\pi ^{2}x^{2}=-4$$

Dividing by \pi ^{2} undoes the multiplication by \pi ^{2}.

$$x^{2}=-\frac{4}{\pi ^{2}}$$

Take the square root of both sides of the equation.

$$x=\frac{2i}{\pi } x=-\frac{2i}{\pi }$$

The equation is now solved.

$$x=\frac{2i}{\pi } x=\frac{-2i}{\pi }$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$\pi \pi x^{2}+4=0$$

Multiply \pi and \pi to get \pi ^{2}.

$$\pi ^{2}x^{2}+4=0$$

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

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

Square 0.

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

Multiply -4 times \pi ^{2}.

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

Multiply -4\pi ^{2} times 4.

$$x=\frac{0±\sqrt{-16\pi ^{2}}}{2\pi ^{2}}$$

Take the square root of -16\pi ^{2}.

$$x=\frac{0±4\pi i}{2\pi ^{2}}$$

Now solve the equation x=\frac{0±4\pi i}{2\pi ^{2}} when ± is plus.

$$x=\frac{2i}{\pi }$$

Now solve the equation x=\frac{0±4\pi i}{2\pi ^{2}} when ± is minus.

$$x=\frac{-2i}{\pi }$$

The equation is now solved.

$$x=\frac{2i}{\pi } x=\frac{-2i}{\pi }$$