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

You entered:

There are no solutions in the real number domain.

There are two complex solutions: x = 0.28787878787879 + 0.089637572471206

where

(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) \(x=--38\pm\frac{\sqrt{-38^2-4*66*6}}{2*66}\)

which simplifies to:

(4) \(x=--38\pm\frac{\sqrt{1444-1584}}{132}\)

(5) \(x=--38\pm\frac{\sqrt{-140}}{132}\)

This means that our solution will require finding the square root of a negative number. There is no real number solution for this, so our solution will be a complex number (that is, it will involve the imaginary number

Let's calculate the square root:

(6) \(x=--38\pm\frac{11.832159566199i}{132}\)

This equation further simplifies to:

(7) \(x=-\frac{--38}{132}\pm0.089637572471206i\)

Solving for x, we find two solutions which are both complex numbers:

x = 0.28787878787879 + 0.089637572471206

and

x = 0.28787878787879 - 0.089637572471206

Both of these solutions are complex numbers.

These are the two solutions that will satisfy the equation

ax

where x is unknown. A, b, and c are constants. The constants a and b are called coefficients. Further, a cannot equal zero in the equation ax

Compared to solving a linear equation, solving a quadratic equation is a more complicated task. Fortunately, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be quickly 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. Here is the quadratic formula:

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, the two roots may be equal, producing one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to compute answers to many real-world problems. The distance before a vehicle can stop once you hit the brakes is one example of an application of quadratic equations.

As mentioned above, in the equation ax

We this quadratic equation calculator is useful to you. We encourage you to plug in different values for a, b, and c. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for your interest in Quadratic-Equation-Calculator.com.

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