3x^2+44x+21=0

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Solution for 3x^2+44x+21=0 equation: 


Simplifying
3x2 + 44x + 21 = 0

Reorder the terms:
21 + 44x + 3x2 = 0

Solving
21 + 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'.
7 + 14.66666667x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 14.66666667x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 14.66666667x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 14.66666667x + x2 = 0 + -7
14.66666667x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
14.66666667x + x2 = -7

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 = -7 + 53.77777780

Reorder the terms:
53.77777780 + 14.66666667x + x2 = -7 + 53.77777780

Combine like terms: -7 + 53.77777780 = 46.7777778
53.77777780 + 14.66666667x + x2 = 46.7777778

Factor a perfect square on the left side:
(x + 7.333333335)(x + 7.333333335) = 46.7777778

Calculate the square root of the right side: 6.839428178

Break this problem into two subproblems by setting 
(x + 7.333333335) equal to 6.839428178 and -6.839428178.


Subproblem 1
x + 7.333333335 = 6.839428178

Simplifying
x + 7.333333335 = 6.839428178

Reorder the terms:
7.333333335 + x = 6.839428178

Solving
7.333333335 + x = 6.839428178

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 = 6.839428178 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + x = 6.839428178 + -7.333333335
x = 6.839428178 + -7.333333335

Combine like terms: 6.839428178 + -7.333333335 = -0.493905157
x = -0.493905157

Simplifying
x = -0.493905157


Subproblem 2
x + 7.333333335 = -6.839428178

Simplifying
x + 7.333333335 = -6.839428178

Reorder the terms:
7.333333335 + x = -6.839428178

Solving
7.333333335 + x = -6.839428178

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 = -6.839428178 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + x = -6.839428178 + -7.333333335
x = -6.839428178 + -7.333333335

Combine like terms: -6.839428178 + -7.333333335 = -14.172761513
x = -14.172761513

Simplifying
x = -14.172761513


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.493905157, -14.172761513}

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