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

A quadratic equation is any function
ax2 + bx + c = 0.
\ In this equation, x is unknown. A, b, and c are constants. The constants a and b are called coefficients. Also, a cannot equal zero. If a=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 quadratic equation may appear daunting, because both x and x2 are unknown. Fortunately, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. The quadratic formula is:


Since there are always 2 solutions to a square root (one negative, one positive), solving the quadratic equation results in 2 values for x. The two solutions for x (which may be positive or negative, real or complex) are called roots. 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. The acceleration of an object as it falls to earth 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.

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