(x+5)2x=52

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Solution for (x+5)2x=52 equation: 


Simplifying
(x + 5) * 2x = 52

Reorder the terms:
(5 + x) * 2x = 52

Reorder the terms for easier multiplication:
2x(5 + x) = 52
(5 * 2x + x * 2x) = 52
(10x + 2x2) = 52

Solving
10x + 2x2 = 52

Solving for variable 'x'.

Reorder the terms:
-52 + 10x + 2x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-26 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-26 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-26 + 5x + x2 = 0

Solving
-26 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 5x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + 5x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 5x + x2 = 0 + 26
5x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
5x + x2 = 26

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 = 26 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 26 + 6.25

Combine like terms: 26 + 6.25 = 32.25
6.25 + 5x + x2 = 32.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
x + 2.5 = 5.678908346

Simplifying
x + 2.5 = 5.678908346

Reorder the terms:
2.5 + x = 5.678908346

Solving
2.5 + x = 5.678908346

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 = 5.678908346 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.678908346 + -2.5
x = 5.678908346 + -2.5

Combine like terms: 5.678908346 + -2.5 = 3.178908346
x = 3.178908346

Simplifying
x = 3.178908346


Subproblem 2
x + 2.5 = -5.678908346

Simplifying
x + 2.5 = -5.678908346

Reorder the terms:
2.5 + x = -5.678908346

Solving
2.5 + x = -5.678908346

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 = -5.678908346 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.678908346 + -2.5
x = -5.678908346 + -2.5

Combine like terms: -5.678908346 + -2.5 = -8.178908346
x = -8.178908346

Simplifying
x = -8.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.178908346, -8.178908346}
Solution
x = {3.178908346, -8.178908346}

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