CurriculumGrade 11Mathematics

Solving Quadratic Equations

Aligned to A-REI.B.4 — Common Core State Standards for Mathematics.

What this lesson teaches

Quadratics can be solved by factoring, taking square roots, completing the square, or the quadratic formula. Completing the square turns the equation into a perfect square you can undo with a root.

Worked example

Solve x^2 + 6x + 4 = 0 by completing the square. Move the constant: x^2 + 6x = −4. Add (6/2)^2 = 9 to both sides: x^2 + 6x + 9 = 5, so (x + 3)^2 = 5. Then x + 3 = ±√5, giving x = −3 ± √5.

Practice questions

  1. Solve x^2 − 5x + 6 = 0 by factoring.
  2. Solve x^2 = 20 by taking square roots.
  3. Solve 2x^2 + 4x − 3 = 0 with the quadratic formula.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Resolver Ecuaciones Cuadráticas

Las cuadráticas se pueden resolver factorizando, sacando raíces cuadradas, completando el cuadrado o con la fórmula cuadrática. Completar el cuadrado convierte la ecuación en un cuadrado perfecto que puedes deshacer con una raíz.

Ejemplo: Resuelve x^2 + 6x + 4 = 0 completando el cuadrado. Mueve la constante: x^2 + 6x = −4. Suma (6/2)^2 = 9 a ambos lados: x^2 + 6x + 9 = 5, así que (x + 3)^2 = 5. Entonces x + 3 = ±√5, dando x = −3 ± √5.

More Algebra lessons

Zeros and Factors of PolynomialsA-APR.B.3Rewriting Expressions (Completing the Square)A-SSE.B.3Sum of a Finite Geometric SeriesA-SSE.B.4The Remainder TheoremA-APR.B.2Proving Polynomial IdentitiesA-APR.C.4Rewriting Rational ExpressionsA-APR.D.6

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