A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.
What is a quadratic equation? A quadratic equation is any equation that has the form: ax2
+ bx + c = 0. In this equation, x is a variable which is not known, and a, b, and c are constants. The constants a and b, are referred to as coefficients. Additionally, it should be mentioned that a cannot equal to 0 in the equation ax2
+bx+c=0. If a equals 0, then ax2
=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 x2
are unknown. However, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula
. The quadratic formula is written:
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, both roots may be the same, producing one solution for x.
Why do we need to be able to solve quadratic equations? Quadratic equations are needed to compute answers to many real-world problems. For example, to calculate 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 x2
(x squared) is what makes this equation quadratic.
We this quadratic equation solver is useful to you. We hope the explanations showing how you can solve the equation yourself are educational and helpful. 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.
for a random example of a quadratic equation.