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

### Notes

A quadratic equation is an equation that can be written as: ax

^{2} + bx + c = 0. In this equation, a, b, and c are constants. X is an unknown. The constants a and b, are referred to as coefficients. Furthermore, it is worth pointing out that a cannot be zero in the equation ax

^{2}+bx+c=0. If a equals 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.

Solving a linear equation is simple. Solving a quadratic equation is less so. However, any quadratic equation can reliably be solved using the

quadratic formula. The quadratic formula is:

Since there are always 2 solutions to a square root (one negative, one positive), solving the quadratic equation results in 2 values for x. The two solutions for x (which may be positive or negative, real or complex) are called roots. Under extraordinary circumstances, the two roots may equal each other, meaning there will only be one solution for x.

Why do we care about qudratic equations? Quadratic equations are needed to compute answers to many real-world problems. For example, to calculate the path of an accelerating object 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 hope you find this quadratic equation calculator useful. We encourage you to plug in different values for a, b, and c. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for your interest in Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.