5(x-6)(x-6)=10

Solution for 5(x-6)(x-6)=10 equation:

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

Reorder the terms:
5(-6 + x)(x + -6) = 10

Reorder the terms:
5(-6 + x)(-6 + x) = 10

Multiply (-6 + x) * (-6 + x)
5(-6(-6 + x) + x(-6 + x)) = 10
5((-6 * -6 + x * -6) + x(-6 + x)) = 10
5((36 + -6x) + x(-6 + x)) = 10
5(36 + -6x + (-6 * x + x * x)) = 10
5(36 + -6x + (-6x + x2)) = 10

Combine like terms: -6x + -6x = -12x
5(36 + -12x + x2) = 10
(36 * 5 + -12x * 5 + x2 * 5) = 10
(180 + -60x + 5x2) = 10

Solving
180 + -60x + 5x2 = 10

Solving for variable 'x'.

Reorder the terms:
180 + -10 + -60x + 5x2 = 10 + -10

Combine like terms: 180 + -10 = 170
170 + -60x + 5x2 = 10 + -10

Combine like terms: 10 + -10 = 0
170 + -60x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(34 + -12x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(34 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
34 + -12x + x2 = 0

Solving
34 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -12x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + -12x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -12x + x2 = 0 + -34
-12x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
-12x + x2 = -34

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 = -34 + 36

Reorder the terms:
36 + -12x + x2 = -34 + 36

Combine like terms: -34 + 36 = 2
36 + -12x + x2 = 2

Factor a perfect square on the left side:
(x + -6)(x + -6) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -6) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + -6 = 1.414213562

Simplifying
x + -6 = 1.414213562

Reorder the terms:
-6 + x = 1.414213562

Solving
-6 + x = 1.414213562

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 = 1.414213562 + 6

Combine like terms: -6 + 6 = 0
0 + x = 1.414213562 + 6
x = 1.414213562 + 6

Combine like terms: 1.414213562 + 6 = 7.414213562
x = 7.414213562

Simplifying
x = 7.414213562

Subproblem 2
x + -6 = -1.414213562

Simplifying
x + -6 = -1.414213562

Reorder the terms:
-6 + x = -1.414213562

Solving
-6 + x = -1.414213562

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 = -1.414213562 + 6

Combine like terms: -6 + 6 = 0
0 + x = -1.414213562 + 6
x = -1.414213562 + 6

Combine like terms: -1.414213562 + 6 = 4.585786438
x = 4.585786438

Simplifying
x = 4.585786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.414213562, 4.585786438}
Solution
x = {7.414213562, 4.585786438}