Exercise
$\left(x^2+y^2+y+x=r^2\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the equation x^2+y^2yx=r^2. Group the terms of the equation. Factor the polynomial y^2+y. Add and subtract \left(\frac{b}{2}\right)^2, where in this case b equals 1. Now we can factor y^2+x+\frac{1}{4} as a squared binomial of the form \left(x+\frac{b}{2}\right)^2. Calculate the power \sqrt{\frac{1}{4}}.
Solve the equation x^2+y^2yx=r^2
Final answer to the exercise
$y=-\frac{1}{2}+\sqrt{r^2-x^2-x+\frac{1}{4}},\:y=-\frac{1}{2}-\sqrt{r^2-x^2-x+\frac{1}{4}}$