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

You entered:

There are two real solutions: x = 1.2136766677411, and x = -0.10841350984634.

(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) \(x=--84\pm\frac{\sqrt{-84^2-4*76*-10}}{2*76}\)

which simplifies to:

(4) \(x=--84\pm\frac{\sqrt{7056--3040}}{152}\)

\(x=\frac{--84+100.47885349664}{152}\) = 1.2136766677411,

and

\(x=\frac{--84-100.47885349664}{152}\) = -0.10841350984634,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

ax

where a, b, and c are constants. X is a variable which is not known. A and b are referred to as coefficients. Also, it should be pointed out that a cannot be 0 in the equation ax

Solving 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. Rarely, these two roots may equal each other, producing one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to find answers to many real-world problems. The laws of motion 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 hope you find this quadratic equation solver useful. We encourage you to try it with different values, and to read the explanation for how to reach your answer. 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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