# Quadratic Formula Calculator

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Table of contents:

## What is a quadratic equation?

A quadratic equation is one which can be written in the form ax²+bx+c=0 where a, b and c are numbers, a ≠ 0, and x is the unknown whose value(s) we wish to find. It cannot have terms involving higher powers of x, like x3. It cannot have terms like 1/x in it.

## How do you solve a quadratic equation?

To solve a quadratic equation we must find values of the unknown x which make the left-hand and right-hand sides equal. Such values are known as solutions or roots of the quadratic equation. Note the difference between solving quadratic equations in comparison to solving linear equations. A quadratic equation will generally have two values of x (solutions) which satisfy it whereas a linear equation only has one solution.

## How to solve a quadratic equation by factorisation?

Write the equation in the correct form. To be in the correct form, you must remove all parentheses from each side of the equation by distributing, combine all like terms, and finally set the equation equal to zero with the terms written in descending order. Use a factoring strategies to factor the problem. Use the Zero Product Property and set each factor containing a variable equal to zero. Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.

## How to solve a quadratic equation by completing the square?

Write the equation in the correct form. To be in the correct form, you must remove all parentheses from each side of the equation by distributing, combine all like terms, and finally set the equation equal to zero with the terms written in descending order. Divide all terms by a (the coefficient of x²). Move the number term (c/a) to the right side of the equation. Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation. We now have something that looks like (x+p)²=q, which can be solved rather easily: Take the square root on both sides of the equation. Subtract the number that remains on the left side of the equation to find x.

## How to solve a quadratic equation by using the quadratic formula?

ax²+bx+c=0...where a, b, and c are the numerical coefficients of the terms of the quadratic, the value of the variable x is given by the following equation: x=(-b∓√(b²-4ac))/2a