A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.

You entered:

There are two real solutions: x = 0.57903596890156, and x = -1.0326442163242.

(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) \(x=-44\pm\frac{\sqrt{44^2-4*97*-58}}{2*97}\)

which simplifies to:

(4) \(x=-44\pm\frac{\sqrt{1936--22504}}{194}\)

\(x=\frac{-44+156.3329779669}{194}\) = 0.57903596890156,

and

\(x=\frac{-44-156.3329779669}{194}\) = -1.0326442163242,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

Finding a solution to a quadratic equation can appear daunting. However, any quadratic equation can reliably be solved using the quadratic formula. This 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. Rarely, the two roots may be equal, meaning there will only be one solution for x.

Quadratic equations have real-life applications. Quadratic equations are needed to calculate answers to many real-world problems. For example, to compute the path of an accelerating object would require the use of s quadratic equation.

The term "quadratic" comes from the Latin word

We this quadratic equation calculator is useful to you. 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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