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 = -0.69491525423729 + 0.78663060243202

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) \(x=-82\pm\frac{\sqrt{82^2-4*59*65}}{2*59}\)

which simplifies to:

(4) \(x=-82\pm\frac{\sqrt{6724-15340}}{118}\)

(5) \(x=-82\pm\frac{\sqrt{-8616}}{118}\)

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) \(x=-82\pm\frac{92.822411086978i}{118}\)

This equation further simplifies to:

(7) \(x=-\frac{-82}{118}\pm0.78663060243202i\)

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

x = -0.69491525423729 + 0.78663060243202

and

x = -0.69491525423729 - 0.78663060243202

Both of these solutions are complex numbers.

These are the two solutions that will satisfy the equation

ax

\ In this equation, a, b, and c are constants. X is a variable which is not known. A and b are referred to as coefficients. Also, a cannot equal to 0 in the equation ax

Finding a solution to a quadratic equation may appear daunting, because both x and x

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

Quadratic equations have real-life applications. Quadratic equations are needed to calculate answers to many real-world problems. For example, to calculate whether a braking car can stop fast enough to avoid hitting something would require the use of s quadratic equation.

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

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