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 = 0.28787878787879 + 0.089637572471206

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) \(x=--38\pm\frac{\sqrt{-38^2-4*66*6}}{2*66}\)

which simplifies to:

(4) \(x=--38\pm\frac{\sqrt{1444-1584}}{132}\)

(5) \(x=--38\pm\frac{\sqrt{-140}}{132}\)

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) \(x=--38\pm\frac{11.832159566199i}{132}\)

This equation further simplifies to:

(7) \(x=-\frac{--38}{132}\pm0.089637572471206i\)

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

x = 0.28787878787879 + 0.089637572471206

and

x = 0.28787878787879 - 0.089637572471206

Both of these solutions are complex numbers.

These are the two solutions that will satisfy the equation

ax

where x is an unknown. A, b, and c are constants. The constants a and b are called coefficients. Also, it should be pointed out that a cannot be equal to zero.

Finding a solution to a quadratic equation may appear daunting. Fortunately, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be readily solved using the quadratic formula, which is the same technique used by this quadratic equation solver. Try it, and it will explain each of the steps to you. 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. Rarely, these two roots may be the same, meaning there will only be one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to calculate answers to many real-world problems. For example, to calculate how an object will rise and fall due to Earth's gravity would require the use of s quadratic equation.

In our equation, a cannot be zero. However, b can be zero, and so can c.

We hope you find this quadratic equation calculator 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.

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