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

Calculating a solution to a quadratic equation may appear daunting, because both x and x

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. Depending on the values of a, b, and c, both roots may equal each other, resulting in one solution for x.

Quadratic equations have real-life applications. Quadratic equations are needed to find answers in many real-world fields, including engineering, biology and business.

The term "quadratic" comes from the Latin word

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