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

ax

\ In this equation, a, b, and c are constants. X is unknown. A and b are called coefficients. Interestingly, a cannot be zero in the equation ax

Calculating a solution to a quadratic equation can seem challenging. Fortunately, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be reliably 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:

Solving a quadratic equation will always result in 2 solutions for x. These solutions are called roots. These roots may both be real numbers or, they may both be complex numbers. Rarely, the two roots may be the same, resulting in one solution for x.

So what? Why do we care about qudratic equations? Quadratic equations are needed to compute answers to many real-world problems. For example, to calculate the path of an accelerating object 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 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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