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, x is a variable which is not known. A, b, and c are constants. A and b are called coefficients. It should be noted that a cannot equal to zero in the equation ax

Solving a linear equation is simple. Solving a quadratic equation is less simple. However, you have this handy-dandy quadratic equation calculator. All kidding aside, quadratic equations can be reliably 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. The quadratic formula is:

When you compute a solution to a quadratic equation, you will always find 2 values for x, called "roots". These roots may both be real numbers or, they may both be complex numbers. Rarely, both roots may have the same value, producing one solution for x.

Quadratic equations are more than just mathematical chores we have to endure. Quadratic equations are needed to find 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.

The term "quadratic" comes from the Latin word

We this quadratic equation calculator is useful to you. We hope the explanations showing how you can solve the equation yourself are educational and helpful. 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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