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:

a
 
x2
 
+
b
 
x
 
+
c
 
= 0
Reset

You entered:
42x2+-44x+94=0.

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:
(2)          

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

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
  and
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.






Notes

What is a quadratic equation? A quadratic equation is an equation that has the form: ax2 + bx + c = 0. In this equation, a, b, and c are constants. X is a variable which is not known. The constants a and b are called coefficients. Also, it should be pointed out that a cannot be equal to zero in the equation ax2+bx+c=0. If a equals 0, then ax2=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.

Solving a linear equation is pretty simple. Solving a quadratic equation requires some more advanced mathematics. However, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be always solved using the quadratic formula, which is the same technique used by this quadratic equation calculator. Try it, and it will explain each of the steps to you. The quadratic formula is:


When you compute a solution to a quadratic equation, you will always find 2 values for x, called "roots". These roots may both be real numbers or, they may both be complex numbers. Under extraordinary circumstances, these two roots may be equal, meaning there will only be one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to find 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.

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

We hope you find this quadratic equation calculator 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.

click here for a random example of a quadratic equation.