![]() Optional: Check answer by substituting each solution separately into the original equation to see if a mistake has been made. Use your knowledge and skills to help others succeed.ĭon't be wasteful protect our environment. Write the quadratic equation in standard form, \(ax2+bx+c0\). Please include it as a link on your website or as a reference in your report, document, or thesis.Īlgebra topics Solving Quadratic Equations by Factoring (Notice: The School for Champions may earn commissions from book purchases) In such a case, you can try to solve the equation by the completing the square method or by using the quadratic equation formula. ![]() Some quadratic equations are not readily factored. Each factor can then be set to 0 and solved for x. Sometimes they are the same solution and the equation degrades to a single solution. The method requires that you first put the equation in the form of ax 2 +īx + c. The general form of a quadratic equation is. For example, the first expression in the equation x 2 + 8x + 15 = 0 can be factored into (x + 3)(x + 5), and then those two factors can then be readily solved for x. Solving Quadratic Equations by Factoring. One method of solving a quadratic equation is by factoring it into two linear equations and then solving each of those equations. In such a case, you can try solving by the Completing the Square method or the Quadratic Formula method. You really can't factor x 2 − 5x + 3 with rational numbers. ![]() There are some quadratic equations where solving by factoring is not effective. X = −2 When solving by factoring does not work You can factor the expression 2x 2 − 3x − 14 into (2x − 7)(x + 2). Since (x + 3)*0 = 0 and 0*(x + 5) = 0, you can set both expressions equal to zero and solve:Īnother example of solving by factoring is the equation: Seeing that 3 * 5 = 15 and 3 + 5 = 8, you can factor the expression x 2 + 8x + 15 into (x + 3)(x + 5). Set each expression equal to 0 and solve them for x to get our two solutions:Ĭonsider the quadratic equation x 2 + 8x + 15 = 0. The standard form of a quadratic equation of one variable is ax 2 +įactoring the quadratic expression ax 2 + bx + c consists of breaking the expression into two sub-expressions in the form of (dx + e)(fx + g).
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