Having been used in several different cultures, the formula has been part of the base of mathematics theory. One of the most fundamental and key principles of mathematics has been the quadratic formula. It has stretched across the world from the Far East, migrating into the Western Hemisphere. Beginning in the “Before Christ” era, the Babylonians were the first to have been recorded demonstrating the equation, circa 400 BC.Throughout the years, the history of mathematics has taken its fair share of changes. You CAN influence the world.The equation is one of the most prominent ideas in mathematics, and is the center of foundation of mathematics itself. Use your knowledge and skills to help others succeed.ĭon't be wasteful protect our environment. (Notice: The School for Champions may earn commissions from book purchases)Ĭlick on a button to bookmark or share this page through Twitter, Facebook, email, or other services: You can use trial and error, factoring, completing the square, or the quadratic formula to solve a quadratic equation. The goal is to find values of x that will provide a solution to the equation. There are preferred ways a quadratic equation should be formatted. (See Using the Quadratic Equation Formula for more information.) SummaryĪ quadratic equation is in the form of ax 2 + bx + c = 0. (See Solving Quadratic Equations by Completing the Square Method for more information.) Quadratic formulaĪnother method is to use the quadratic formula, which states that for the quadratic equation ax 2 + bx + c = 0, the solutions for x can be determined from the formula: Then by taking the square root, you can get your solutions. The method involves rearranging the equation and adding a term to both sides of the equal sign in order to make the left side a squared expression. Completing the squareĬompleting the square is another way to find solutions. This leads to the solutions of x = −1 and x = −2. One common method to solve a quadratic equation is by factoring the left expression into two sub-expressions and then solving each of those.įor example, x 2 + 3x + 2 = 0 can be readily factored into (x + 1)(x + 2) = 0. Standard methods to solve quadratic equations are: You can use trial and error to find solutions to a quadratic equation, but that certainly is not the best method to use. In some cases, the two solutions are the same, so it is actually just one solution. Note that for a quadratic equation, there are usually two solutions. You can substitute each number back into the equation to verify that they are solutions. In other words, for a quadratic equation, you want to find the values of x that would result in ax 2 + bx + c equaling 0.įor example, solutions to the equation x 2 + 3x + 2 = 0 are x = −1 and x = −2. Likewise, x 2 + x/3 + 1/4 = 0, should be multiplied by 12 to put it in the form ofĪ major objective in Algebra is to find the solutions to equations. You should multiply each side of the equation by 10 to put it in the more desirable form of x 2 + 53x − 4 = 0. If they are fractions or decimals, it is desirable to multiply the equation by some number to make a, b and c integers.įor example, consider the equation 0.1x 2 + 5.3x − 0.4 = 0. −2x 2 + x − 4 = 0 by −1 so that it becomes 2x 2 − x + 4 = 0. If a is negative, you can multiply both sides of the equation by −1.įor example, you can multiply both sides of the equation "a" should be positiveĪlthough a can be either positive or negative, it is preferred to put the equation in the form where a is a positive number. X 2 + x + 5 = 0 by subtracting x 2 − 4 from both sides of the equation.Ģx 2 − x = 7 + 3x should be put in the form of 2x 2 − 4x − 7 = 0 by subtracting 7 + 3x from both sides of the equation. The equation 3x 2 + x + 1 = x 2 − 4 should be put in the form of The expression on the right side of the equal sign must equal 0 to be in the proper quadratic equation format. There is a definite format for the quadratic equation. ( See Linear Equations for more information.) Put in proper format The following equations are not quadratic equations, because a = 0.ģx 2 − 3x 2 + x + 5 = 0 because 3x 2 − 3x 2 = 0, resulting in x + 5 = 0 If a = 0, the equation becomes an equation of the first degree or a linear equation of the form bx + c = 0. a, b and c represent positive or negative numbersĪ quadratic equation is considered an equation of the second degree, because of the x 2 term.The quadratic equation is in the form of:
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