Question

write the equation in standard form for the circle $x^{2}+y^{2}+2x - 15 = 0$.

Explanation:

Step1: Group x-terms, isolate constants

$x^2 + 2x + y^2 = 15$

Step2: Complete the square for x

Take half of 2, square it: $(\frac{2}{2})^2=1$. Add to both sides.
$x^2 + 2x + 1 + y^2 = 15 + 1$

Step3: Rewrite as perfect squares

$(x+1)^2 + y^2 = 16$

Answer:

$(x+1)^2 + y^2 = 16$