#SOLVE THE QUADRATIC EQUATION HOW TO#

Step - 1: Get the equation into standard form.The step-by-step process of solving the quadratic equations by completing the square is explained along with an example. Similar to quadratic equations we have solutions for linear equations, which are used to solve linear programming problems.Ĭompleting the square means writing the quadratic expression ax 2 + bx + c into the form a (x - h) 2 + k (which is also known as vertex form), where h = -b/2a and 'k' can be obtained by substituting x = h in ax 2 + bx + c. If it is NOT factorable, then we can use one of the other methods as explained below. This method is applicable only when the quadratic expression is factorable. Thus, the solutions of the quadratic equation x 2 - 3x + 2 = 0 are 1 and 2. Step - 4: Solve each of the above equations.Įxample: Solve the quadratic equation x 2 - 3x + 2 = 0 by factoring it.įactoring the left side part, we get (x - 1) (x - 2) = 0.Step - 3: By zero product property, set each of the factors to zero.

#SOLVE THE QUADRATIC EQUATION HOW TO#

If you want to know how to factor a quadratic expression, click here.

Step - 2: Factor the quadratic expression.

i.e., Get all the terms of to one side (usually to left side) of the equation such that the other side is 0. The step-by-step process of solving quadratic equations by factoring is explained along with an example. Solving quadratics by factoring is one of the famous methods used to solve quadratic equations. Now, we will learn the methods of solving the quadratic equations in each of the above-mentioned methods. Thus, the roots of the equation are 0 and -11. Thus, the roots of the equation are 0 and 5. The process is explained with examples below. To solve this type of equation, we simply factor x out from the left side, set each of the factors to zero, and solve. In a quadratic equation ax 2 + bx + c = 0, if the term with c is missing then the equation becomes ax 2 + bx = 0. (note that these are imaginary (or) complex numbers). Thus, the roots of the equation are 7i and -7i. Thus, the roots of the equation are 2 and -2.

This can be solved by taking square root on both sides. In a quadratic equation ax 2 + bx + c = 0, if the term with b is missing then the equation becomes ax 2 + c = 0. Solving quadratic equations by quadratic formulaĪpart from these methods, there are some other methods that are used only in specific cases (when the quadratic equation has missing terms) as explained below.Solving quadratic equations by graphing.Solving quadratic equations by completing the square.Solving quadratic equations by factoring.But how to find them if they are not given? There are different ways of solving quadratic equations.

Thus, x = 1 and x = 2 are the roots of x 2 - 3x + 2 = 0. For example, one can easily see that x = 1 and x = 2 satisfy the quadratic equation x 2 - 3x + 2 = 0 (you can substitute each of the values in this equation and verify). Since the degree of the quadratic equation is 2, it can have a maximum of 2 roots. The value(s) that satisfy the quadratic equation is known as its roots (or) solutions (or) zeros. Solving quadratic equations means finding a value (or) values of variable which satisfy the equation. Solving Quadratic Equations by Quadratic Formula Solving Quadratic Equations by Completing Square Let us learn all the methods in detail here along with a few solved examples. But the most popular method is solving quadratic equations by factoring. There are different methods used to solve quadratic equations. We know that any value(s) of x that satisfies the equation is known as a solution (or) root of the equation and the process of finding the values of x which satisfy the equation ax 2 + bx + c = 0 is known as solving quadratic equations. The standard form of a quadratic equation is given by the equation ax 2 + bx + c = 0, where a ≠ 0. It means the quadratic equation has a variable raised to 2 as the greatest power term. The word 'quadratic' is originated from the word 'quad' and its meaning is 'square'.

Before going to learn about solving quadratic equations, let us recall a few facts about quadratic equations.