Find the square root of both sides of the equation. Add (b/2) 2 to both sides of the equation to form a perfect square on the left side of the equation.
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By completing the square: Put the equation in the form of ax 2 + bx -c (make a -1 by dividing if necessary). Keep it handy while you’re revising the concept, especially before an exam. There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square. By using the quadratic formula: Plug into the formula. This one page PDF covers summarised theory and the most important formulas related to the concept. Cheat sheets on Graph Transformations ( Basic and Advanced) are also available on this website. There are three main ways to solve quadratic equations: 1) to factor the quadratic equation if you can do so, 2) to use the quadratic formula, or 3) to complete the square. The problems typically involved solving a pair of simultaneous equations of the form : x + y = p, xy = q, which are equivalent to the equation x 2 – px + q = 0. In 628 AD, Brahmagupta, an Indian mathematician, gave the first explicit solution of the quadratic equation ax 2 + bx = c. In 1637, René Descartes published La Geometrie containing the quadratic formula in the form we know today.Ī good knowledge of plotting graphs of functions will help quite a bit in solving problems related to quadratic equations. A quadratic equation always has two roots, which may be real or imaginary, depending upon the values of a, b, and c.īabylonian mathematicians, as early as 2000 BC, could solve problems relating the areas and sides of rectangles. The values of the variable that satisfy the equation are called the roots of the equation.
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This cheat sheet covers the high school math concept – Quadratic Equations.Īn equation of the form ax 2 + bx + c = 0 (where a ≠ 0) is known as a quadratic equation.