A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.

### Notes

What is a quadratic equation? A quadratic equation is an equation

ax

^{2} + bx + c = 0,

where a, b, and c are constants. X is an unknown. The constants a and b, are referred to as coefficients. Interestingly, a cannot equal zero in the equation ax

^{2}+bx+c=0. If a=0, then ax

^{2}=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.

Calculating a solution to a quadratic equation may appear daunting, because both x and x

^{2} are unknown. However, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be always solved using the

quadratic formula, which is the same technique used by this quadratic equation calculator. Try it, and it will explain each of the steps to you. Here is the quadratic formula:

Solving a quadratic equation will always result in 2 solutions for x. These solutions are called roots. These roots may both be real numbers or, they may both be complex numbers. Rarely, the two roots may be equal, resulting in one solution for x.

So what? Why do we care about qudratic equations? Quadratic equations are needed to find answers to many real-world problems. For example, to compute how an object will rise and fall due to Earth's gravity would require the use of s quadratic equation.

The term "quadratic" comes from the Latin word

*quadratum,* which means "square." Why? Because what defines a quadratic equation is the inclusion of some variable squared. In our equation above, the term x

^{2} (x squared) is what makes this equation quadratic.

We this quadratic equation solver is useful to you. We encourage you to try it with different values, and to read the explanation for how to reach your answer. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for using Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.