Quadratic Formula
The quadratic formula solves any quadratic equation — it is on the GED formula sheet, so you don’t need to memorize it.
This is a free explanation of Quadratic Formula — a preview, not the full interactive lesson. The lesson, practice, quizzes, and AI Tutor are inside the app.
Use the quadratic formula when factoring is difficult, when a is not 1, or when the answer is not a whole number. It works for any quadratic in standard form ax² + bx + c = 0. The formula is x = (−b ± √(b² − 4ac)) / 2a.
Label your equation first: a is the coefficient of x², b is the coefficient of x, and c is the constant. Then substitute carefully, simplify the square root, and split into two answers — one using + and one using −.
Be careful with signs when substituting, especially with negative values of b or c. The part under the square root, b² − 4ac, is the discriminant: if it is positive there are 2 real solutions, if zero there is 1, and if negative there are no real solutions.
Worked example
Solve with the formula: x² − x − 6 = 0
- Identify a, b, and c: a = 1, b = −1, c = −6.
- Substitute into the formula: x = (−(−1) ± √((−1)² − 4(1)(−6))) / 2(1).
- Simplify under the square root: 1 + 24 = 25, and √25 = 5, giving x = (1 ± 5) / 2.
- Split into two answers: x = (1 + 5)/2 = 3, or x = (1 − 5)/2 = −2.
x = 3 or x = −2
On the test: On the GED & HiSET the formula is provided on the formula sheet; label a, b, c carefully before substituting.
Inside the app, Quadratic Formula comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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