# Solving 55x2+-33x+25 using the Quadratic Formula

For your equation of the form "ax2 + bx + c = 0," enter the values for a, b, and c:

 a x2 + b x + c = 0
Reset

You entered:
55x2+-33x+25=0.

There are no solutions in the real number domain.
There are two complex solutions: x = 0.3 + 0.60377599699347i, and x = 0.3 - 0.60377599699347i,
where i is the imaginary unit.

## Here's how we found that solution:

You entered the following equation:
(1)           55x2+-33x+25=0.

For any quadratic equation ax2 + bx + c = 0, one can solve for x using the following equation, which is known as the quadratic formula:
(2)

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:
(3)           $$x=--33\pm\frac{\sqrt{-33^2-4*55*25}}{2*55}$$

which simplifies to:
(4)           $$x=--33\pm\frac{\sqrt{1089-5500}}{110}$$

Now, note that b2-4ac is a negative number. Specifically in our case, 1089 - 5500 = -4411.
(5)           $$x=--33\pm\frac{\sqrt{-4411}}{110}$$

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 i, defined as the square root of -1.).
Let's calculate the square root:
(6)           $$x=--33\pm\frac{66.415359669281i}{110}$$

This equation further simplifies to:
(7)           $$x=-\frac{--33}{110}\pm0.60377599699347i$$

Solving for x, we find two solutions which are both complex numbers:
x = 0.3 + 0.60377599699347i
and
x = 0.3 - 0.60377599699347i

Both of these solutions are complex numbers.
These are the two solutions that will satisfy the equation 55x2+-33x+25=0.

### Notes

A quadratic equation is any equation
ax2 + bx + c = 0.
\ In this equation, x is a variable of unknown value. A, b, and c are constants. A and b are called coefficients. Interestingly, a cannot be equal to 0 in the equation ax2+bx+c=0.

Solving a linear equation is pretty simple. Solving a quadratic equation requires some more advanced mathematics. Fortunately, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. Here is the quadratic formula:

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

Quadratic equations have real-life applications. Quadratic equations are needed to find answers to many real-world problems. For example, to calculate how an object will rise and fall due to Earth's gravity 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 this quadratic equation solver is useful to you. We hope the explanations showing how you can solve the equation yourself are educational and helpful. 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.