62=2x+2x(5+x)

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Solution for 62=2x+2x(5+x) equation: 


Simplifying
62 = 2x + 2x(5 + x)
62 = 2x + (5 * 2x + x * 2x)
62 = 2x + (10x + 2x2)

Combine like terms: 2x + 10x = 12x
62 = 12x + 2x2

Solving
62 = 12x + 2x2

Solving for variable 'x'.

Reorder the terms:
62 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
62 + -12x + -2x2 = 0 + 2x2 + -2x2
62 + -12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
62 + -12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(31 + -6x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(31 + -6x + -1x2)' equal to zero and attempt to solve:

Simplifying
31 + -6x + -1x2 = 0

Solving
31 + -6x + -1x2 = 0

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

Divide each side by '-1'.
-31 + 6x + x2 = 0

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 6x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + 6x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 6x + x2 = 0 + 31
6x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
6x + x2 = 31

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 31 + 9

Reorder the terms:
9 + 6x + x2 = 31 + 9

Combine like terms: 31 + 9 = 40
9 + 6x + x2 = 40

Factor a perfect square on the left side:
(x + 3)(x + 3) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 3) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + 3 = 6.32455532

Simplifying
x + 3 = 6.32455532

Reorder the terms:
3 + x = 6.32455532

Solving
3 + x = 6.32455532

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 6.32455532 + -3

Combine like terms: 3 + -3 = 0
0 + x = 6.32455532 + -3
x = 6.32455532 + -3

Combine like terms: 6.32455532 + -3 = 3.32455532
x = 3.32455532

Simplifying
x = 3.32455532


Subproblem 2
x + 3 = -6.32455532

Simplifying
x + 3 = -6.32455532

Reorder the terms:
3 + x = -6.32455532

Solving
3 + x = -6.32455532

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -6.32455532 + -3

Combine like terms: 3 + -3 = 0
0 + x = -6.32455532 + -3
x = -6.32455532 + -3

Combine like terms: -6.32455532 + -3 = -9.32455532
x = -9.32455532

Simplifying
x = -9.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.32455532, -9.32455532}
Solution
x = {3.32455532, -9.32455532}

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