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

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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:
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 function ax2 + bx + c = 0, where a, b, and c are constants. X is a variable which is not known. The constants a and b, are referred to as coefficients. Interestingly, a cannot be zero. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a linear equation is relatively straightforward. Solving a quadratic equation is not quite so straightforward. Fortunately, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be reliably 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:


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. Depending on the values of a, b, and c, the two roots may be the same, resulting in one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to find answers to many real-world problems. The acceleration of an object as it falls to earth 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 this quadratic equation calculator 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 using Quadratic-Equation-Calculator.com.

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