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

You entered:

There are two real solutions: x = -1.4545454545455, and x = -3.

(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) \(x=-98\pm\frac{\sqrt{98^2-4*22*96}}{2*22}\)

which simplifies to:

(4) \(x=-98\pm\frac{\sqrt{9604-8448}}{44}\)

\(x=\frac{-98+34}{44}\) = -1.4545454545455,

and

\(x=\frac{-98-34}{44}\) = -3,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

ax

\ In this equation, a, b, and c are constants. X is unknown. A and b are referred to as coefficients. Furthermore, it should be mentioned that a cannot equal to zero. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Compared to solving a linear equation, solving a quadratic equation is a more complicated task. However, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be always 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. Here is the quadratic formula:

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, both roots may have the same value, meaning there will only be one solution for x.

Quadratic equations are more than just mathematical mumbo-jumbo Quadratic equations are needed to calculate answers to many real-world problems. For example, to calculate how an object will rise and fall due to Earth's gravity would require the use of s quadratic equation.

Because equations can be rearranged without losing their meaning, sometimes you may see an equation that isn't written exactly this way, but it's still a quadratic equation. For example, you probably know that

ax

Here are some other examples of ways to write the quadratic equation. They all mean the same thing:

(1) \(ax^2+bx=d\), where d = -c

(2) \(x^2+bx-d=e\), where a=1 and d=e-c

(3) \(ax^2=ex+d\), where d=-c and e=-b

(4) \(\frac{x^2}{f}-d=ex\), where d=-c and e=-b and \(f=\frac{1}{a}\)

Look at each of the examples above. Do you understand why they are still quadratic equations, and how they can be rearranged to look like our familiar formula?

We hope you find this quadratic equation calculator useful. We encourage you to plug in different values for a, b, and c. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for your interest in Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.