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 an function that can be written as:
+ bx + c = 0.
\ In this equation, x is an unknown. A, b, and c are constants. A and b are referred to as coefficients. It should be noted that a cannot equal zero. If a=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 challenging. However, you have this handy-dandy quadratic equation calculator. All kidding aside, quadratic equations can be quickly 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. The quadratic formula is written:
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. Rarely, these two roots may be the same, meaning there will only be one solution for x.
Who cares? Why do we care about qudratic equations? Quadratic equations are needed to calculate answers to many real-world problems. The contour of a parablolic mirror is one example of an application of quadratic equations.
As mentioned above, in the equation ax2
+bx+c=0, a cannot be zero. If a were 0, then ax2
= 0 for any value of x, so our equation becomes 0 + bx + c = 0, which is the same as bx + c = 0, which is no longer a quadratic equation. In fact, bx + c = 0 is a linear equation, which is much simpler to solve than a quadratic equation.
We this quadratic equation calculator 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, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for using Quadratic-Equation-Calculator.com.
for a random example of a quadratic equation.