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

### Notes

A quadratic equation is an function that can be written in the form:

ax

^{2} + bx + c = 0,

where x is a variable of unknown value. A, b, and c are constants. A and b are referred to as coefficients. It is worth pointing out that a cannot be zero. 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 quadratic equation may appear daunting, because both x and x

^{2} are unknown. Fortunately, there are a number of methods for solving quadratic equations. One of the most widely used is the

quadratic formula. The quadratic formula is:

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. Under extraordinary circumstances, these two roots may equal each other, resulting in one solution for x.

Quadratic equations are important. Quadratic equations are needed to find answers in many real-world fields, including physics, biology and architecture.

As mentioned above, in the equation ax

^{2}+bx+c=0, a cannot be zero. If a were 0, then ax

^{2} = 0x

^{2} = 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 hope you find this quadratic equation solver useful. 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.

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