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 = 0.30722891566265 + 0.66009914051486

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) \(x=--51\pm\frac{\sqrt{-51^2-4*83*44}}{2*83}\)

which simplifies to:

(4) \(x=--51\pm\frac{\sqrt{2601-14608}}{166}\)

(5) \(x=--51\pm\frac{\sqrt{-12007}}{166}\)

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) \(x=--51\pm\frac{109.57645732547i}{166}\)

This equation further simplifies to:

(7) \(x=-\frac{--51}{166}\pm0.66009914051486i\)

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

x = 0.30722891566265 + 0.66009914051486

and

x = 0.30722891566265 - 0.66009914051486

Both of these solutions are complex numbers.

These are the two solutions that will satisfy the equation

Compared to solving a linear equation, solving a quadratic equation is a more complicated task. Fortunately, any quadratic equation can always be solved using the quadratic formula. 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. Depending on the values of a, b, and c, both roots may have the same value, resulting in one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to calculate answers to many real-world problems. The acceleration of an object as it falls to earth is one example of an application of quadratic equations.

The term "quadratic" comes from the Latin word

We hope you find this quadratic equation solver useful. We encourage you to plug in different values for a, b, and c. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for your interest in Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.