Step 1) Write the quadratic equation in standard form. Either will work as a solution.Įxample 2: Solve each quadratic equation using factoring. Step 3) Use the zero-product property and set each factor with a variable equal to zero: We want to subtract 18 away from each side of the equation: Use the zero-product property and set each factor with a variable equal to zeroĮxample 1: Solve each quadratic equation using factoring.Place the quadratic equation in standard form.In either scenario, the equation would be true:Ġ = 0 Solving a Quadratic Equation using Factoring To do this, we set each factor equal to zero and solve:Įssentially, x could be 2 or x could be -3. This means we can use our zero-product property. The result of this multiplication is zero. In this case, we have a quantity (x - 2) multiplied by another quantity (x + 3). We can apply this to more advanced examples. Y could be 0, x could be a non-zero number X could be 0, y could be a non-zero number The zero product property tells us if the product of two numbers is zero, then at least one of them must be zero: Quadratic Formula: x b±b2 4ac 2a x b ± b 2 4 a c 2 a. For equations with real solutions, you can use the graphing tool to visualize the solutions. Often the easiest method of solving a quadratic equation is factoring. Created by Sal Khan and Monterey Institute for Technology and Education. The Quadratic Formula Calculator finds solutions to quadratic equations with real coefficients. Sal solves the equation s2-2s-350 by factoring the expression on the left as (s+5) (s-7) and finding the s-values that make each factor equal to zero. This works based on the zero-product property (also known as the zero-factor property). Step 1: Enter the equation you want to solve using the quadratic formula. When a quadratic equation is in standard form and the left side can be factored, we can solve the quadratic equation using factoring. For these types of problems, obtaining a solution can be a bit more work than what we have seen so far. Some examples of a quadratic equation are:ĥx 2 + 18x + 9 = 0 Zero-Product Property Up to this point, we have not attempted to solve an equation in which the exponent on a variable was not 1. Generally, we think about a quadratic equation in standard form:Ī ≠ 0 (since we must have a variable squared)Ī, b, and c are any real numbers (a can't be zero) A quadratic equation is an equation that contains a squared variable and no other term with a higher degree. We will expand on this knowledge and learn how to solve a quadratic equation using factoring. They are used in countless ways in the fields of engineering, architecture, finance, biological science, and, of course, mathematics. For example, equations such as 2x2 + 3x 1 0 2 x 2 + 3 x 1 0 and x2 4 0 x 2 4 0 are quadratic equations. A quadratic expression contains a squared variable and no term with a higher degree. An equation containing a second-degree polynomial is called a quadratic equation. Over the course of the last few lessons, we have learned to factor quadratic expressions.
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