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

You entered:

There are two real solutions: x = 1.2264870422407, and x = -0.87648704224065.

(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) \(x=--28\pm\frac{\sqrt{-28^2-4*80*-86}}{2*80}\)

which simplifies to:

(4) \(x=--28\pm\frac{\sqrt{784--27520}}{160}\)

\(x=\frac{--28+168.2379267585}{160}\) = 1.2264870422407,

and

\(x=\frac{--28-168.2379267585}{160}\) = -0.87648704224065,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

ax

where x is unknown, and a, b, and c are constants. A and b are referred to as coefficients. Further, a cannot equal to zero. If a=0, then ax

Solving a quadratic equation can appear challenging. Fortunately, any quadratic equation can reliably be solved using the quadratic formula. The quadratic formula is:

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, both roots may be the same, meaning there will only be one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to calculate answers to many real-world problems. The laws of motion is one example of an application of quadratic equations.

In our equation, a cannot be zero. However, b can be zero, and so can c.

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 using Quadratic-Equation-Calculator.com.

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