solving quadratic equations by factoring steps

#Solving quadratic equations by factoring steps how to

To identify the difference of two squares, the quadratic should be made up of two terms separated by a minus sign.įor the quadratic, this is the same as. Quadratic equations of the form can be solved using the difference of two squares method. Therefore the solutions are 𝑥=a and 𝑥=-a.

#Solving quadratic equations by factoring steps how to

How to Solve Quadratic Equations with Difference of Two SquaresĪny quadratic equation of the form 𝑥 2-a 2=0 can be factored as (𝑥+a)(𝑥-a)=0 using the difference of two squares. Therefore the factored quadratic is and so, and. The two numbers that add to make -3 and multiply to make -10 are 2 and -5. Therefore the factored quadratic is and so, or. The two numbers that add to make 2 and multiply to make -3 are 3 and -1. Here c is negative so the quadratic will factor as. The two numbers that add to make -5 and multiply to make 6 are -3 and -2. Here, c is positive and b is negative so the quadratic will factor as. Therefore, the factored quadratic is and so, and. The two numbers that add to make 6 and multiply to make 8 are 4 and 2. Since b and c are positive, the quadratic will factor as. Here are some examples of solving quadratic equations by factoring. It is easier to factorise quadratics if you know what signs to expect in the brackets.

If c is negative, one number will be positive and one number will be negative.

If c is positive but b is negative, the two numbers will both be negative.

If b and c are both positive, the two numbers will both be positive.

To solve a quadratic by factoring, think of two numbers that add to make the coefficient of 𝑥 and multiply to make the constant term.įor a quadratic, use the following rules to find the two numbers: Solving Quadratic Equations by Factoring: Examples with Negatives Therefore the solutions to this quadratic equation are 𝑥=-3 and 𝑥=-1. We find the values of 𝑥 that make each bracket equal zero. Solve the quadratic by setting each bracket equal to zero Therefore the quadratic equation can be factorised to. In step 1, the two numbers that add to make 4 and multiply to make 3 were 1 and 3. Factor the quadratic as (𝑥+ m)(𝑥+ n)=0, where m and n are the two numbers from step 1 The numbers 1 and 3 add to make 4 and multiply to make 3. Think of two numbers that add to make b and multiply to make c Solving Quadratic Equations by Factoring: Example 1įor example, solve the quadratic equation by factoring.

Solve the quadratic by setting each bracket equal to zero.Factor the quadratic as (𝑥+ m)(𝑥+ n)=0, where m and n are the two numbers from step 1.Think of two numbers that add to make b and multiply to make c.How to Solve Quadratic Equations by Factoring To solve a quadratic equation ‘𝑥 2+ b𝑥+c=0′ by factoring: The next step is to square root both sides of the equation so that 𝑥=±√5.Įvaluating ±√5 on a calculator, 𝑥≈-2.24 or 𝑥≈2.24. The first step is to add 5 to both sides of the equation so that 𝑥 2=5. We still square root both sides of the equation to obtain the solution. In this next example, 𝑥 2 is equal to a non square number. This simple type of quadratic equation can be identified as there is only an 𝑥 2 and constant term in the equation. If a quadratic equation is of the form 𝑥 2 =k, square root both sides. How to Solve Quadratic Equations using Square Roots Īll quadratic equations can be solved using the quadratic formula so this method will always work for solving quadratic equations. If the quadratic cannot be factorised, use the quadratic formula.If the quadratic cannot be factorised, complete the square and solve.

If the quadratic contains an 𝑥 2 coefficient greater than 1, try to split the 𝑥 term and factorise by grouping.

Solve by setting each factor to equal zero.

Try to factorise by finding two numbers that add to make the coefficient of 𝑥 and multiply to make the constant term.

If the quadratic only contains 𝑥 2 and 𝑥 terms, factorise the 𝑥 out and solve.

If 𝑥 2 equals a number, square root both sides of the equation to solve it.

Here is a list of the methods that can be used to solve quadratic equations: If the quadratic has an 𝑥 2 coefficient greater than 1 or cannot be factorised, the quadratic formula can be used: