(x+6)(x+6)=10

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Solution for (x+6)(x+6)=10 equation: 


Simplifying
(x + 6)(x + 6) = 10

Reorder the terms:
(6 + x)(x + 6) = 10

Reorder the terms:
(6 + x)(6 + x) = 10

Multiply (6 + x) * (6 + x)
(6(6 + x) + x(6 + x)) = 10
((6 * 6 + x * 6) + x(6 + x)) = 10
((36 + 6x) + x(6 + x)) = 10
(36 + 6x + (6 * x + x * x)) = 10
(36 + 6x + (6x + x2)) = 10

Combine like terms: 6x + 6x = 12x
(36 + 12x + x2) = 10

Solving
36 + 12x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
36 + -10 + 12x + x2 = 10 + -10

Combine like terms: 36 + -10 = 26
26 + 12x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
26 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + 12x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + 12x + x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 12x + x2 = 0 + -26
12x + x2 = 0 + -26

Combine like terms: 0 + -26 = -26
12x + x2 = -26

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -26 + 36

Reorder the terms:
36 + 12x + x2 = -26 + 36

Combine like terms: -26 + 36 = 10
36 + 12x + x2 = 10

Factor a perfect square on the left side:
(x + 6)(x + 6) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 6) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 6 = 3.16227766

Simplifying
x + 6 = 3.16227766

Reorder the terms:
6 + x = 3.16227766

Solving
6 + x = 3.16227766

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 3.16227766 + -6

Combine like terms: 6 + -6 = 0
0 + x = 3.16227766 + -6
x = 3.16227766 + -6

Combine like terms: 3.16227766 + -6 = -2.83772234
x = -2.83772234

Simplifying
x = -2.83772234


Subproblem 2
x + 6 = -3.16227766

Simplifying
x + 6 = -3.16227766

Reorder the terms:
6 + x = -3.16227766

Solving
6 + x = -3.16227766

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -3.16227766 + -6

Combine like terms: 6 + -6 = 0
0 + x = -3.16227766 + -6
x = -3.16227766 + -6

Combine like terms: -3.16227766 + -6 = -9.16227766
x = -9.16227766

Simplifying
x = -9.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.83772234, -9.16227766}

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