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

\ In this equation, x is unknown. A, b, and c are constants. The constants a and b are called coefficients. Also, a cannot equal zero. If a=0, then ax

Solving a quadratic equation may appear daunting, because both x and x

Since there are always 2 solutions to a square root (one negative, one positive), solving the quadratic equation results in 2 values for x. The two solutions for x (which may be positive or negative, real or complex) are called roots. Rarely, these two roots may be the same, meaning there will only be one solution for x.

Quadratic equations have real-life applications. 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.

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

We this quadratic equation solver is useful to you. We encourage you to try it with different values, and to read the explanation for how to reach your answer. 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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