6(x+6)=x(x+5)

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Solution for 6(x+6)=x(x+5) equation: 


Simplifying
6(x + 6) = x(x + 5)

Reorder the terms:
6(6 + x) = x(x + 5)
(6 * 6 + x * 6) = x(x + 5)
(36 + 6x) = x(x + 5)

Reorder the terms:
36 + 6x = x(5 + x)
36 + 6x = (5 * x + x * x)
36 + 6x = (5x + x2)

Solving
36 + 6x = 5x + x2

Solving for variable 'x'.

Combine like terms: 6x + -5x = 1x
36 + 1x + -1x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
36 + 1x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
36 + 1x + -1x2 = 0 + x2 + -1x2
36 + 1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36 + 1x + -1x2 = 0

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

Divide each side by '-1'.
-36 + -1x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -1x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -1x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1x + x2 = 0 + 36
-1x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-1x + x2 = 36

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 36 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 36 + 0.25

Combine like terms: 36 + 0.25 = 36.25
0.25 + -1x + x2 = 36.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + -0.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
x + -0.5 = 6.020797289

Simplifying
x + -0.5 = 6.020797289

Reorder the terms:
-0.5 + x = 6.020797289

Solving
-0.5 + x = 6.020797289

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 6.020797289 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 6.020797289 + 0.5
x = 6.020797289 + 0.5

Combine like terms: 6.020797289 + 0.5 = 6.520797289
x = 6.520797289

Simplifying
x = 6.520797289


Subproblem 2
x + -0.5 = -6.020797289

Simplifying
x + -0.5 = -6.020797289

Reorder the terms:
-0.5 + x = -6.020797289

Solving
-0.5 + x = -6.020797289

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -6.020797289 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -6.020797289 + 0.5
x = -6.020797289 + 0.5

Combine like terms: -6.020797289 + 0.5 = -5.520797289
x = -5.520797289

Simplifying
x = -5.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.520797289, -5.520797289}

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