![]() If this is possible (it is not always), then we can solve the quadratic equation by setting each expression equal to 0 and solving for x. The goal of factoring a quadratic equation is to decompose a quadratic equation in standard form into a product of expressions that produces the quadratic equation. Once it is, factoring the quadratic equation involves some inspection, and possibly some trial and error. Using factoring to solve a quadratic equation involves first ensuring that the quadratic equation is in standard form. For example, given that the graph of a quadratic equation crosses the x-axis at (2, 0), x = 2 is a solution to the quadratic equation. The x-values at these points are the solution(s) to the quadratic equation. ![]() Granted that you have access to a graph of a given quadratic equation, solving the equation only requires you to find the roots, or the point(s) at which the graph crosses the x-axis. If the quadratic equation is easy to graph by hand, it will likely be simpler to use another method to solve the equation. Graphing a quadratic equation is another way to easily solve the equation, assuming that you have access to a graphing calculator or graphing software. In many cases however, we will not have a perfect square, and this method of solving quadratic equations cannot be used. There are other types of quadratic equations that can be solved in this way, such as: The above is a solution to a very simple quadratic equation. However, it is only possible in a very limited number of cases where the quadratic equation involves perfect squares. Computing a square root:Ĭomputing a square root of a quadratic equation that is a perfect square is arguably the simplest way to solve a quadratic equation. Deciding which method to use is a large part of solving quadratic equations because depending on the specific quadratic equation, certain methods may be easier or more efficient to use. There are a number of different methods for solving a quadratic equation, such as computing the square root, factoring, completing the square, using the quadratic formula, or graphing the equation. As long as an expression can be re-written such that it takes on the form above, it is a quadratic equation, even if it is not originally in standard form. Quadratic equations can take on a number of different forms the form above is referred to as the standard form of a quadratic equation. In other words, to be a quadratic equation, the expression must include an x 2 term, and cannot include a higher order term such as x 3, x 7, etc. Being a "second-degree algebraic expression" means that the highest order variable term in the equation must have an order of 2, and that this term must exist. Where x represents an unknown, a, b, and c are constants, and a≠0 this is because if a = 0, there will be no second-degree term, and the equation will therefore not be quadratic. ![]() To use the calculator, please provide values for a, b, and c, then click the "Solve" button.Ī quadratic equation is a second-degree algebraic expression that can be written in the form, This quadratic formula calculator solves quadratic equations of the form ax 2 + bx + c = 0 and shows the solving process using the quadratic formula.
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