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

\ In this equation, x is unknown, and a, b, and c are constants. The constants a and b are called coefficients. It is worth noting 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 be equal, resulting in one solution for x.

Quadratic equations are more than just mathematical chores we have to endure. Quadratic equations are needed to compute answers to many real-world problems. For example, to calculate the path of an accelerating object would require the use of s quadratic equation.

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

We hope you find this quadratic equation solver useful. 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 your interest in Quadratic-Equation-Calculator.com.

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