x(3x+4)=840

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Solution for x(3x+4)=840 equation: 


Simplifying
x(3x + 4) = 840

Reorder the terms:
x(4 + 3x) = 840
(4 * x + 3x * x) = 840
(4x + 3x2) = 840

Solving
4x + 3x2 = 840

Solving for variable 'x'.

Reorder the terms:
-840 + 4x + 3x2 = 840 + -840

Combine like terms: 840 + -840 = 0
-840 + 4x + 3x2 = 0

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

Divide each side by '3'.
-280 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + 1.333333333x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 1.333333333x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 1.333333333x + x2 = 0 + 280
1.333333333x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
1.333333333x + x2 = 280

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 280 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 280 + 0.4444444442

Combine like terms: 280 + 0.4444444442 = 280.4444444442
0.4444444442 + 1.333333333x + x2 = 280.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 280.4444444442

Calculate the square root of the right side: 16.746475583

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 16.746475583 and -16.746475583.


Subproblem 1
x + 0.6666666665 = 16.746475583

Simplifying
x + 0.6666666665 = 16.746475583

Reorder the terms:
0.6666666665 + x = 16.746475583

Solving
0.6666666665 + x = 16.746475583

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 16.746475583 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 16.746475583 + -0.6666666665
x = 16.746475583 + -0.6666666665

Combine like terms: 16.746475583 + -0.6666666665 = 16.0798089165
x = 16.0798089165

Simplifying
x = 16.0798089165


Subproblem 2
x + 0.6666666665 = -16.746475583

Simplifying
x + 0.6666666665 = -16.746475583

Reorder the terms:
0.6666666665 + x = -16.746475583

Solving
0.6666666665 + x = -16.746475583

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -16.746475583 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -16.746475583 + -0.6666666665
x = -16.746475583 + -0.6666666665

Combine like terms: -16.746475583 + -0.6666666665 = -17.4131422495
x = -17.4131422495

Simplifying
x = -17.4131422495


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.0798089165, -17.4131422495}

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