Three Methods Overview

Algebra 1 · Axiom Academy

LESSON Three Ways to Solve a Quadratic Factoring, completing the square, and the quadratic formula — three routes from one equation to the same two roots, and how to pick the fastest one. Take a single quadratic, x^2 + 5x + 6 = 0 . Each method peels it apart differently, yet all three converge on the same two roots . Watch the equation split into three lanes and rejoin at the answer. The general quadratic — the starting point for all three methods Solve x^2 + 5x + 6 = 0 . With a leading coefficient of 1 , look for two numbers that multiply to 6 and add to 5 . The animation tests candidate pairs and locks the one that fits, then splits the factors into roots. Fastest when it works; reveals the root structure directly; sharpens number sense. Only works for equations that factor over the integers; awkward with large or non-integer coefficients. 3. Method 2 — Completing the Square Solve the same equation x^2 + 5x + 6 = 0 . Rewrite it as x^2 + 5x = -6 , then add the magic number to both sides so the left side becomes a perfect square. The animation literally fills in the missing corner of an x^2 square. Works on every quadratic; shows the geometric meaning; hands you the vertex for graphing. More steps than factoring; fractions appear when b is odd; demands careful algebra. 4. Method 3 — The Quadratic Formula

This is the written version of the interactive lesson above. See the full Algebra 1 course.