Solve quadratic equation by factoring how to#

Complete the Square – this method is a long one, but it works.However, some quadratics are difficult to factor, and the quadratic formula would be more helpful in those cases. Factoring– this method is helpful in some cases to avoid the work of graphing, completing the square, or using the quadratic formula.Also, the graph will not intersect the x-axis if the solutions are complex (in the case of a negative discriminant). The only drawback is that it can be difficult to find exact values of x. If you graph the quadratic function f(x) = ax 2 + bx + c, you can find out where it intersects the x-axis. Graphing – this is a good visual method if you have the vertex form of a parabola or if you have a parabola-like curve from a data set.Here are four methods you can use to solve a quadratic equation: We’ll also take a closer look at how these methods are connected to each other.

In this article, we’ll talk about the four methods you can use to solve a quadratic equation and give some examples for each one. However, it might be easier to factor in some cases to avoid radicals and fractions in the quadratic formula. Of course, the quadratic formula will work for any quadratic equation you choose. If factoring is hard, the quadratic formula (a shortcut for completing the square) helps. Graphing gives a good visual, but it is hard to find values of x from a graph with no equation. So, how do you solve quadratic equations? You can solve quadratic equations by graphing, factoring, completing the square, & the quadratic formula. Luckily, there are several ways to do it.

Solve quadratic equation by factoring how to#

In these cases it is usually better to solve by completing the square or using the quadratic formula.Quadratic equations come up often in mathematics and physics, and it is vital to know how to solve them.

$solve quadratic equation by factoring$

However, not all quadratic equations can be factored evenly. Step 4: Set each factor to zero and solve for x.Ģ.2: c = 15, a positive number, therefore both factors will be positive or both factors will be negative.Ģ.3: b = 8, a positive number, therefore the both factors will be positive.Ģ.2: c = -24, a negative number, therefore one factor is negative and the other is positive.Ģ.3: b = 10, a positive number, therefore the larger factor will be positive and the smaller factor negative.įactoring quadratics is generally the easier method for solving quadratic equations. Now that the equation has been factored, solve for x. If c is negative and b is positive, the larger factor will be positive and the smaller will be negative.Ģ.2: c = -14, a negative number, therefore one factor is negative and the other is positive.Ģ.3: b = 5, a positive number, therefore the larger factor will be positive and the smaller will be negative.Ĭreate two sets of parentheses each containing a x and one of the factors. If c is positive and b is negative, both factors will be negative. If both c and b are negative, the larger factor will be negative and the smaller will be positive. If both c and b are positive, both factors will be positive. Now create factor pairsĢ.3: Determine the factor pair that will add to give b. If c is negative then one factor will be positive and the other negative. If c is positive then both factors will be positive or both factors will be negative. Step 2: Determine the factor pair of c that will add to give b.įirst ask yourself what are the factors pairs of c, ignoring the negative sign for now. This equation is already in the proper form where a = 1, b = 5 and c = -14.