2(x+5)2x=58

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Solution for 2(x+5)2x=58 equation: 


Simplifying
2(x + 5) * 2x = 58

Reorder the terms:
2(5 + x) * 2x = 58

Reorder the terms for easier multiplication:
2 * 2x(5 + x) = 58

Multiply 2 * 2
4x(5 + x) = 58
(5 * 4x + x * 4x) = 58
(20x + 4x2) = 58

Solving
20x + 4x2 = 58

Solving for variable 'x'.

Reorder the terms:
-58 + 20x + 4x2 = 58 + -58

Combine like terms: 58 + -58 = 0
-58 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-29 + 10x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-29 + 10x + 2x2)' equal to zero and attempt to solve:

Simplifying
-29 + 10x + 2x2 = 0

Solving
-29 + 10x + 2x2 = 0

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

Divide each side by '2'.
-14.5 + 5x + x2 = 0

Move the constant term to the right:

Add '14.5' to each side of the equation.
-14.5 + 5x + 14.5 + x2 = 0 + 14.5

Reorder the terms:
-14.5 + 14.5 + 5x + x2 = 0 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + 5x + x2 = 0 + 14.5
5x + x2 = 0 + 14.5

Combine like terms: 0 + 14.5 = 14.5
5x + x2 = 14.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 14.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 14.5 + 6.25

Combine like terms: 14.5 + 6.25 = 20.75
6.25 + 5x + x2 = 20.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 20.75

Calculate the square root of the right side: 4.55521679

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.55521679 and -4.55521679.


Subproblem 1
x + 2.5 = 4.55521679

Simplifying
x + 2.5 = 4.55521679

Reorder the terms:
2.5 + x = 4.55521679

Solving
2.5 + x = 4.55521679

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 4.55521679 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.55521679 + -2.5
x = 4.55521679 + -2.5

Combine like terms: 4.55521679 + -2.5 = 2.05521679
x = 2.05521679

Simplifying
x = 2.05521679


Subproblem 2
x + 2.5 = -4.55521679

Simplifying
x + 2.5 = -4.55521679

Reorder the terms:
2.5 + x = -4.55521679

Solving
2.5 + x = -4.55521679

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -4.55521679 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.55521679 + -2.5
x = -4.55521679 + -2.5

Combine like terms: -4.55521679 + -2.5 = -7.05521679
x = -7.05521679

Simplifying
x = -7.05521679


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.05521679, -7.05521679}
Solution
x = {2.05521679, -7.05521679}

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