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 = 0.3 + 0.60377599699347

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) \(x=--33\pm\frac{\sqrt{-33^2-4*55*25}}{2*55}\)

which simplifies to:

(4) \(x=--33\pm\frac{\sqrt{1089-5500}}{110}\)

(5) \(x=--33\pm\frac{\sqrt{-4411}}{110}\)

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) \(x=--33\pm\frac{66.415359669281i}{110}\)

This equation further simplifies to:

(7) \(x=-\frac{--33}{110}\pm0.60377599699347i\)

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

x = 0.3 + 0.60377599699347

and

x = 0.3 - 0.60377599699347

Both of these solutions are complex numbers.

These are the two solutions that will satisfy the equation

ax

where x is an unknown, and a, b, and c are constants. A and b are referred to as coefficients. Also, it should be noted that a cannot equal to zero.

Finding a solution to a quadratic equation can appear challenging. However, any quadratic equation can quickly be solved using the quadratic formula. Here is the quadratic formula:

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. Under extraordinary circumstances, both roots may have the same value, resulting in one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to calculate answers to many real-world problems. The laws of motion 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 hope you find this quadratic equation calculator useful. We encourage you to plug in different values for a, b, and c. 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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