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

where x is an unknown. A, b, and c are constants. A and b are referred to as coefficients. Furthermore, it should be noted that a cannot be equal to 0.

Calculating a solution to a quadratic equation may seem daunting. Fortunately, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be readily solved using the quadratic formula, which is the same technique used by this quadratic equation solver. Try it, and it will explain each of the steps to you. This 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. Under extraordinary circumstances, the two roots may equal each other, producing one solution for x.

Why do we need to be able to solve quadratic equations? Quadratic equations are needed to find answers to many real-world problems. For example, to compute whether a braking car can stop fast enough to avoid hitting something would require the use of s quadratic equation.

As mentioned above, in the equation ax

We hope you find this quadratic equation calculator useful. We encourage you to plug in different values for a, b, and c. 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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