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
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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

What is a quadratic equation? Any equation that can be written in the form:
ax2 + bx + c = 0.
\ In this equation, a, b, and c are constants. X is an unknown. A and b are called coefficients. Interestingly, a cannot equal zero. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Finding a solution to a quadratic equation may appear daunting, because both x and x2 are unknown. Fortunately, any quadratic equation can always be solved using 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 equal, meaning there will only be one solution for x.

So what? Why do we care about qudratic equations? Quadratic equations are needed to calculate 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 ax2+bx+c=0, a cannot be zero. If a were 0, then ax2 = 0x2 = 0 for any value of x, so our equation becomes 0 + bx + c = 0, which is the same as bx + c = 0, which is no longer a quadratic equation. In fact, bx + c = 0 is a linear equation, which is much simpler to solve than a quadratic equation.

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 using Quadratic-Equation-Calculator.com.