3x^2+22x-6279=0

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Solution for 3x^2+22x-6279=0 equation: 


Simplifying
3x2 + 22x + -6279 = 0

Reorder the terms:
-6279 + 22x + 3x2 = 0

Solving
-6279 + 22x + 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'.
-2093 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '2093' to each side of the equation.
-2093 + 7.333333333x + 2093 + x2 = 0 + 2093

Reorder the terms:
-2093 + 2093 + 7.333333333x + x2 = 0 + 2093

Combine like terms: -2093 + 2093 = 0
0 + 7.333333333x + x2 = 0 + 2093
7.333333333x + x2 = 0 + 2093

Combine like terms: 0 + 2093 = 2093
7.333333333x + x2 = 2093

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = 2093 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = 2093 + 13.44444445

Combine like terms: 2093 + 13.44444445 = 2106.44444445
13.44444445 + 7.333333333x + x2 = 2106.44444445

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 2106.44444445

Calculate the square root of the right side: 45.896017741

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 45.896017741 and -45.896017741.


Subproblem 1
x + 3.666666667 = 45.896017741

Simplifying
x + 3.666666667 = 45.896017741

Reorder the terms:
3.666666667 + x = 45.896017741

Solving
3.666666667 + x = 45.896017741

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 45.896017741 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 45.896017741 + -3.666666667
x = 45.896017741 + -3.666666667

Combine like terms: 45.896017741 + -3.666666667 = 42.229351074
x = 42.229351074

Simplifying
x = 42.229351074


Subproblem 2
x + 3.666666667 = -45.896017741

Simplifying
x + 3.666666667 = -45.896017741

Reorder the terms:
3.666666667 + x = -45.896017741

Solving
3.666666667 + x = -45.896017741

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -45.896017741 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -45.896017741 + -3.666666667
x = -45.896017741 + -3.666666667

Combine like terms: -45.896017741 + -3.666666667 = -49.562684408
x = -49.562684408

Simplifying
x = -49.562684408


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.229351074, -49.562684408}

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