Solving 42x2+-44x+94 using the Quadratic Formula

A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.

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

= 0

You entered:

There are no solutions in the real number domain.
There are two complex solutions: x = 0.52380952380952 + 1.4013275209107i, and x = 0.52380952380952 - 1.4013275209107i,
where i is the imaginary unit.

Here's how we found that solution:

You entered the following equation:
(1)           42x2+-44x+94=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:

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:
(3)           \(x=--44\pm\frac{\sqrt{-44^2-4*42*94}}{2*42}\)

which simplifies to:
(4)           \(x=--44\pm\frac{\sqrt{1936-15792}}{84}\)

Now, note that b2-4ac is a negative number. Specifically in our case, 1936 - 15792 = -13856.
(5)           \(x=--44\pm\frac{\sqrt{-13856}}{84}\)

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)           \(x=--44\pm\frac{117.7115117565i}{84}\)

This equation further simplifies to:
(7)           \(x=-\frac{--44}{84}\pm1.4013275209107i\)

Solving for x, we find two solutions which are both complex numbers:
x = 0.52380952380952 + 1.4013275209107i
x = 0.52380952380952 - 1.4013275209107i

Both of these solutions are complex numbers.
These are the two solutions that will satisfy the equation 42x2+-44x+94=0.


A quadratic equation is any equation ax2 + bx + c = 0, where x is an unknown. A, b, and c are constants. The constants a and b are called coefficients. Interestingly, a cannot be zero.

In contrast to solving a linear equation, solving a quadratic equation requires some more advanced mathematics.. However, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be quickly 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. 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, the two roots may be equal, producing one solution for x.

There are many uses for quadratic equations. Quadratic equations are needed to find answers to many real-world problems. For example, to compute the path of an accelerating object would require the use of s quadratic equation.

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

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