Solve pi^2+y^2=4

$$\pi ^ { 2 } + y ^ { 2 } = 4$$

Solve for y

$$y=-i\sqrt{\pi ^{2}-4}\approx -0-2.422726646i$$

$$y=i\sqrt{\pi ^{2}-4}\approx 2.422726646i$$

Steps by Finding Square Root

Subtract \pi ^{2} from both sides.

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

The equation is now solved.

$$y=i\sqrt{\pi ^{2}-4} y=-i\sqrt{\pi ^{2}-4}$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$\pi ^{2}+y^{2}-4=0$$

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.

$$y^{2}+\pi ^{2}-4=0$$

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

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

Square 0.

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

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

$$y=\frac{0±\sqrt{-4\pi ^{2}+16}}{2}$$

Take the square root of -4\pi ^{2}+16.

$$y=\frac{0±2i\sqrt{-\left(-\pi ^{2}+4\right)}}{2}$$

Now solve the equation y=\frac{0±2i\sqrt{-\left(-\pi ^{2}+4\right)}}{2} when ± is plus.

$$y=i\sqrt{\pi ^{2}-4}$$

Now solve the equation y=\frac{0±2i\sqrt{-\left(-\pi ^{2}+4\right)}}{2} when ± is minus.

$$y=-i\sqrt{\pi ^{2}-4}$$

The equation is now solved.

$$y=i\sqrt{\pi ^{2}-4} y=-i\sqrt{\pi ^{2}-4}$$