4340=(x+31)(x)(4)

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Solution for 4340=(x+31)(x)(4) equation: 


Simplifying
4340 = (x + 31)(x)(4)

Reorder the terms:
4340 = (31 + x)(x)(4)

Reorder the terms for easier multiplication:
4340 = 4x(31 + x)
4340 = (31 * 4x + x * 4x)
4340 = (124x + 4x2)

Solving
4340 = 124x + 4x2

Solving for variable 'x'.

Reorder the terms:
4340 + -124x + -4x2 = 124x + -124x + 4x2 + -4x2

Combine like terms: 124x + -124x = 0
4340 + -124x + -4x2 = 0 + 4x2 + -4x2
4340 + -124x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
4340 + -124x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1085 + -31x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1085 + -31x + -1x2)' equal to zero and attempt to solve:

Simplifying
1085 + -31x + -1x2 = 0

Solving
1085 + -31x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1085 + 31x + x2 = 0

Move the constant term to the right:

Add '1085' to each side of the equation.
-1085 + 31x + 1085 + x2 = 0 + 1085

Reorder the terms:
-1085 + 1085 + 31x + x2 = 0 + 1085

Combine like terms: -1085 + 1085 = 0
0 + 31x + x2 = 0 + 1085
31x + x2 = 0 + 1085

Combine like terms: 0 + 1085 = 1085
31x + x2 = 1085

The x term is 31x.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31x + 240.25 + x2 = 1085 + 240.25

Reorder the terms:
240.25 + 31x + x2 = 1085 + 240.25

Combine like terms: 1085 + 240.25 = 1325.25
240.25 + 31x + x2 = 1325.25

Factor a perfect square on the left side:
(x + 15.5)(x + 15.5) = 1325.25

Calculate the square root of the right side: 36.403983299

Break this problem into two subproblems by setting 
(x + 15.5) equal to 36.403983299 and -36.403983299.


Subproblem 1
x + 15.5 = 36.403983299

Simplifying
x + 15.5 = 36.403983299

Reorder the terms:
15.5 + x = 36.403983299

Solving
15.5 + x = 36.403983299

Solving for variable 'x'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + x = 36.403983299 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + x = 36.403983299 + -15.5
x = 36.403983299 + -15.5

Combine like terms: 36.403983299 + -15.5 = 20.903983299
x = 20.903983299

Simplifying
x = 20.903983299


Subproblem 2
x + 15.5 = -36.403983299

Simplifying
x + 15.5 = -36.403983299

Reorder the terms:
15.5 + x = -36.403983299

Solving
15.5 + x = -36.403983299

Solving for variable 'x'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + x = -36.403983299 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + x = -36.403983299 + -15.5
x = -36.403983299 + -15.5

Combine like terms: -36.403983299 + -15.5 = -51.903983299
x = -51.903983299

Simplifying
x = -51.903983299


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.903983299, -51.903983299}
Solution
x = {20.903983299, -51.903983299}

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