Solve 2^2+y^2=1

$$2 ^ { 2 } + y ^ { 2 } = 1$$

Solve for y

$$y=-\sqrt{3}i\approx -0-1.732050808i$$

$$y=\sqrt{3}i\approx 1.732050808i$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

$$4+y^{2}=1$$

Subtract 4 from both sides.

$$y^{2}=1-4$$

Subtract 4 from 1 to get -3.

$$y^{2}=-3$$

The equation is now solved.

$$y=\sqrt{3}i y=-\sqrt{3}i$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

$$4+y^{2}=1$$

Subtract 1 from both sides.

$$4+y^{2}-1=0$$

Subtract 1 from 4 to get 3.

$$3+y^{2}=0$$

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.

$$y^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 3}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 3}}{2}$$

Multiply -4 times 3.

$$y=\frac{0±\sqrt{-12}}{2}$$

Take the square root of -12.

$$y=\frac{0±2\sqrt{3}i}{2}$$

Now solve the equation y=\frac{0±2\sqrt{3}i}{2} when ± is plus.

$$y=\sqrt{3}i$$

Now solve the equation y=\frac{0±2\sqrt{3}i}{2} when ± is minus.

$$y=-\sqrt{3}i$$

The equation is now solved.

$$y=\sqrt{3}i y=-\sqrt{3}i$$