3x^2-44x-5=0

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Solution for 3x^2-44x-5=0 equation: 


Simplifying
3x2 + -44x + -5 = 0

Reorder the terms:
-5 + -44x + 3x2 = 0

Solving
-5 + -44x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-1.666666667 + -14.66666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -14.66666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -14.66666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -14.66666667x + x2 = 0 + 1.666666667
-14.66666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-14.66666667x + x2 = 1.666666667

The x term is -14.66666667x.  Take half its coefficient (-7.333333335).
Square it (53.77777780) and add it to both sides.

Add '53.77777780' to each side of the equation.
-14.66666667x + 53.77777780 + x2 = 1.666666667 + 53.77777780

Reorder the terms:
53.77777780 + -14.66666667x + x2 = 1.666666667 + 53.77777780

Combine like terms: 1.666666667 + 53.77777780 = 55.444444467
53.77777780 + -14.66666667x + x2 = 55.444444467

Factor a perfect square on the left side:
(x + -7.333333335)(x + -7.333333335) = 55.444444467

Calculate the square root of the right side: 7.446102636

Break this problem into two subproblems by setting 
(x + -7.333333335) equal to 7.446102636 and -7.446102636.


Subproblem 1
x + -7.333333335 = 7.446102636

Simplifying
x + -7.333333335 = 7.446102636

Reorder the terms:
-7.333333335 + x = 7.446102636

Solving
-7.333333335 + x = 7.446102636

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '7.333333335' to each side of the equation.
-7.333333335 + 7.333333335 + x = 7.446102636 + 7.333333335

Combine like terms: -7.333333335 + 7.333333335 = 0.000000000
0.000000000 + x = 7.446102636 + 7.333333335
x = 7.446102636 + 7.333333335

Combine like terms: 7.446102636 + 7.333333335 = 14.779435971
x = 14.779435971

Simplifying
x = 14.779435971


Subproblem 2
x + -7.333333335 = -7.446102636

Simplifying
x + -7.333333335 = -7.446102636

Reorder the terms:
-7.333333335 + x = -7.446102636

Solving
-7.333333335 + x = -7.446102636

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '7.333333335' to each side of the equation.
-7.333333335 + 7.333333335 + x = -7.446102636 + 7.333333335

Combine like terms: -7.333333335 + 7.333333335 = 0.000000000
0.000000000 + x = -7.446102636 + 7.333333335
x = -7.446102636 + 7.333333335

Combine like terms: -7.446102636 + 7.333333335 = -0.112769301
x = -0.112769301

Simplifying
x = -0.112769301


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.779435971, -0.112769301}

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