Solve y=sqrt{1-x^2};x=-2

$$y = \sqrt { 1 - x ^ { 2 } } ; x = - 2$$

Solve for y, x (complex solution)

$$x=-2$$

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

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$y=\sqrt{1-\left(-2\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$y=\sqrt{1-4}$$

Subtract 4 from 1 to get -3.

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

Factor -3=3\left(-1\right). Rewrite the square root of the product \sqrt{3\left(-1\right)} as the product of square roots \sqrt{3}\sqrt{-1}. By definition, the square root of -1 is i.

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

The system is now solved.

$$y=\sqrt{3}i x=-2$$