(7x-6)(7x-6)=20

Solution for (7x-6)(7x-6)=20 equation:

Simplifying
(7x + -6)(7x + -6) = 20

Reorder the terms:
(-6 + 7x)(7x + -6) = 20

Reorder the terms:
(-6 + 7x)(-6 + 7x) = 20

Multiply (-6 + 7x) * (-6 + 7x)
(-6(-6 + 7x) + 7x * (-6 + 7x)) = 20
((-6 * -6 + 7x * -6) + 7x * (-6 + 7x)) = 20
((36 + -42x) + 7x * (-6 + 7x)) = 20
(36 + -42x + (-6 * 7x + 7x * 7x)) = 20
(36 + -42x + (-42x + 49x2)) = 20

Combine like terms: -42x + -42x = -84x
(36 + -84x + 49x2) = 20

Solving
36 + -84x + 49x2 = 20

Solving for variable 'x'.

Reorder the terms:
36 + -20 + -84x + 49x2 = 20 + -20

Combine like terms: 36 + -20 = 16
16 + -84x + 49x2 = 20 + -20

Combine like terms: 20 + -20 = 0
16 + -84x + 49x2 = 0

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

Divide each side by '49'.
0.3265306122 + -1.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.3265306122' to each side of the equation.
0.3265306122 + -1.714285714x + -0.3265306122 + x2 = 0 + -0.3265306122

Reorder the terms:
0.3265306122 + -0.3265306122 + -1.714285714x + x2 = 0 + -0.3265306122

Combine like terms: 0.3265306122 + -0.3265306122 = 0.0000000000
0.0000000000 + -1.714285714x + x2 = 0 + -0.3265306122
-1.714285714x + x2 = 0 + -0.3265306122

Combine like terms: 0 + -0.3265306122 = -0.3265306122
-1.714285714x + x2 = -0.3265306122

The x term is -1.714285714x.  Take half its coefficient (-0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
-1.714285714x + 0.7346938773 + x2 = -0.3265306122 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714x + x2 = -0.3265306122 + 0.7346938773

Combine like terms: -0.3265306122 + 0.7346938773 = 0.4081632651
0.7346938773 + -1.714285714x + x2 = 0.4081632651

Factor a perfect square on the left side:
(x + -0.857142857)(x + -0.857142857) = 0.4081632651

Calculate the square root of the right side: 0.638876565

Break this problem into two subproblems by setting 
(x + -0.857142857) equal to 0.638876565 and -0.638876565.

Subproblem 1
x + -0.857142857 = 0.638876565

Simplifying
x + -0.857142857 = 0.638876565

Reorder the terms:
-0.857142857 + x = 0.638876565

Solving
-0.857142857 + x = 0.638876565

Solving for variable 'x'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + x = 0.638876565 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = 0.638876565 + 0.857142857
x = 0.638876565 + 0.857142857

Combine like terms: 0.638876565 + 0.857142857 = 1.496019422
x = 1.496019422

Simplifying
x = 1.496019422

Subproblem 2
x + -0.857142857 = -0.638876565

Simplifying
x + -0.857142857 = -0.638876565

Reorder the terms:
-0.857142857 + x = -0.638876565

Solving
-0.857142857 + x = -0.638876565

Solving for variable 'x'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + x = -0.638876565 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = -0.638876565 + 0.857142857
x = -0.638876565 + 0.857142857

Combine like terms: -0.638876565 + 0.857142857 = 0.218266292
x = 0.218266292

Simplifying
x = 0.218266292

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.496019422, 0.218266292}