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 = 0.52380952380952 + 1.4013275209107

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) \(x=--44\pm\frac{\sqrt{-44^2-4*42*94}}{2*42}\)

which simplifies to:

(4) \(x=--44\pm\frac{\sqrt{1936-15792}}{84}\)

(5) \(x=--44\pm\frac{\sqrt{-13856}}{84}\)

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) \(x=--44\pm\frac{117.7115117565i}{84}\)

This equation further simplifies to:

(7) \(x=-\frac{--44}{84}\pm1.4013275209107i\)

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

x = 0.52380952380952 + 1.4013275209107

and

x = 0.52380952380952 - 1.4013275209107

Both of these solutions are complex numbers.

These are the two solutions that will satisfy the equation

Solving a linear equation is relatively straightforward. Solving a quadratic equation is not quite so straightforward. Fortunately, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be reliably solved using the quadratic formula, which is the same technique used by this quadratic equation calculator. 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. Depending on the values of a, b, and c, the two roots may be the same, resulting in one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to find 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.

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 using Quadratic-Equation-Calculator.com.

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