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 = -0.024691358024691 + 0.68448969262366

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) \(x=-4\pm\frac{\sqrt{4^2-4*81*38}}{2*81}\)

which simplifies to:

(4) \(x=-4\pm\frac{\sqrt{16-12312}}{162}\)

(5) \(x=-4\pm\frac{\sqrt{-12296}}{162}\)

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) \(x=-4\pm\frac{110.88733020503i}{162}\)

This equation further simplifies to:

(7) \(x=-\frac{-4}{162}\pm0.68448969262366i\)

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

x = -0.024691358024691 + 0.68448969262366

and

x = -0.024691358024691 - 0.68448969262366

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 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. Here is the quadratic formula:

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, the two roots may have the same value, resulting in one solution for x.

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

As mentioned above, in the equation ax

We this quadratic equation calculator 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 your interest in Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.