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

Solving a linear equation is rather straightforward. Solving a quadratic equation requires some more advanced mathematics. 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 written:

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. Under extraordinary circumstances, both roots may equal each other, meaning there will only be one solution for x.

Quadratic equations have real-life applications. Quadratic equations are needed to calculate answers to many real-world problems. For example, to compute the path of an accelerating object would require the use of s quadratic equation.

The quadratic equation calculator on this website uses the quadratic formula to solve your quadratic equations, and this is a reliable and relatively simple way to do it. But there are other ways to solve a quadratic equation, such as completing the square or factoring.

We this quadratic equation solver 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.

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