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

ax

where x is a variable which is not known, and a, b, and c are constants. The constants a and b are called coefficients. Additionally, it is worth noting that a cannot be equal to zero. If a is 0, then ax

In contrast to solving a linear equation, solving a quadratic equation requires a few more steps. However, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be reliably 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. The quadratic formula is:

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. Under extraordinary circumstances, the two roots may have the same value, producing one solution for x.

Why do we care about qudratic equations? Quadratic equations are needed to calculate answers to many real-world problems. The contour of a parablolic mirror is one example of an application of quadratic equations.

The quadratic equation calculator on this website uses the quadratic formula to solve your quadratic equations, and this is a reliable and relatively simple way to do it. But there are other ways to solve a quadratic equation, such as completing the square or factoring.

We this quadratic equation solver is useful to you. 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 using Quadratic-Equation-Calculator.com.

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