Write the quadratic in standard form: (ax^2+bx+c)
Factor out (a) from the (x^2) and (x) terms: (aleft(x^2+frac{b}{a}xright)+c)
Take half of the coefficient of (x) inside the parentheses and square it: (left(frac{1}{2}cdotfrac{b}{a}right)^2=frac{b^2}{4a^2})
Add and subtract that value inside the parentheses:
(aleft(x^2+frac{b}{a}x+frac{b^2}{4a^2}-frac{b^2}{4a^2}right)+c)
Rewrite the perfect square:
(aleft(left(x+frac{b}{2a}right)^2-frac{b^2}{4a^2}right)+c)
Distribute (a) and combine constants:
(aleft(x+frac{b}{2a}right)^2-frac{b^2}{4a}+c)
Final completed-square form:
(aleft(x+frac{b}{2a}right)^2+left(c-frac{b^2}{4a}right))