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

You entered:

There are no solutions in the real number domain.

There are two complex solutions: x = -0.21951219512195 + 0.62517100575494

where

(1)

For any quadratic equation

(2)

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:

(3) \(x=-18\pm\frac{\sqrt{18^2-4*41*18}}{2*41}\)

which simplifies to:

(4) \(x=-18\pm\frac{\sqrt{324-2952}}{82}\)

(5) \(x=-18\pm\frac{\sqrt{-2628}}{82}\)

This means that our solution will require finding the square root of a negative number. There is no real number solution for this, so our solution will be a complex number (that is, it will involve the imaginary number

Let's calculate the square root:

(6) \(x=-18\pm\frac{51.264022471905i}{82}\)

This equation further simplifies to:

(7) \(x=-\frac{-18}{82}\pm0.62517100575494i\)

Solving for x, we find two solutions which are both complex numbers:

x = -0.21951219512195 + 0.62517100575494

and

x = -0.21951219512195 - 0.62517100575494

Both of these solutions are complex numbers.

These are the two solutions that will satisfy the equation

Finding a solution to a quadratic equation can appear challenging. However, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be reliably 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:

When you compute a solution to a quadratic equation, you will always find 2 values for x, called "roots". These roots may both be real numbers or, they may both be complex numbers. Rarely, these two roots may equal each other, resulting in one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to calculate answers in many real-world fields, including engineering, pharmacokinetics and business.

The term "quadratic" comes from the Latin word

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 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.