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

You entered:

There are two real solutions: x = 0.42105263157895, and x = 0.2.

(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) \(x=--59\pm\frac{\sqrt{-59^2-4*95*8}}{2*95}\)

which simplifies to:

(4) \(x=--59\pm\frac{\sqrt{3481-3040}}{190}\)

\(x=\frac{--59+21}{190}\) = 0.42105263157895,

and

\(x=\frac{--59-21}{190}\) = 0.2,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

ax

\ In this equation, x is a variable of unknown value. A, b, and c are constants. The constants a and b, are referred to as coefficients. It should be mentioned that a cannot equal 0 in the equation ax

Calculating a solution to 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. Depending on the values of a, b, and c, these two roots may be equal, resulting in one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to compute answers to many real-world problems. For example, to compute the path of an accelerating object 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 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 your interest in Quadratic-Equation-Calculator.com.

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