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

ax

where x is a variable of unknown value. A, b, and c are constants. A and b are referred to as coefficients. Further, it is worth pointing out that a cannot equal zero. If a is equal to 0, then ax

Compared to solving a linear equation, solving a quadratic equation requires some more advanced mathematics.. Fortunately, any quadratic equation can readily 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 be the same, producing one solution for x.

Why do we need to be able to solve quadratic equations? Quadratic equations are needed to calculate answers in many real-world fields, including physics, pharmacokinetics and business.

The quadratic formula has been known for centuries. Brahmagupta, a mathematician from India, first described the quadratic formula as a means to calculate solutions to quadratic equations in the 7th Century AD.

We hope you find this quadratic equation solver 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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