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

You entered:

There are two real solutions: x = -1.5389902381335, and x = -16.461009761866.

(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) \(x=-54\pm\frac{\sqrt{54^2-4*3*76}}{2*3}\)

which simplifies to:

(4) \(x=-54\pm\frac{\sqrt{2916-912}}{6}\)

\(x=\frac{-54+44.766058571199}{6}\) = -1.5389902381335,

and

\(x=\frac{-54-44.766058571199}{6}\) = -16.461009761866,

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 a variable which is not known. The constants a and b are called coefficients. Further, it is worth pointing out that a cannot be equal to 0 in the equation ax

Solving a linear equation is straightforward. Solving a quadratic equation requires some more advanced mathematics. Fortunately, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be readily solved using the quadratic formula, which is the same technique used by this quadratic equation solver. Try it, and it will explain each of the steps to you. 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. Rarely, the two roots may have the same value, meaning there will only be one solution for x.

Why do we need to be able to solve quadratic equations? Quadratic equations are needed to calculate 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.

As mentioned above, in the equation ax

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