(7x-2)(7x-2)=60

Solution for (7x-2)(7x-2)=60 equation:

Simplifying
(7x + -2)(7x + -2) = 60

Reorder the terms:
(-2 + 7x)(7x + -2) = 60

Reorder the terms:
(-2 + 7x)(-2 + 7x) = 60

Multiply (-2 + 7x) * (-2 + 7x)
(-2(-2 + 7x) + 7x * (-2 + 7x)) = 60
((-2 * -2 + 7x * -2) + 7x * (-2 + 7x)) = 60
((4 + -14x) + 7x * (-2 + 7x)) = 60
(4 + -14x + (-2 * 7x + 7x * 7x)) = 60
(4 + -14x + (-14x + 49x2)) = 60

Combine like terms: -14x + -14x = -28x
(4 + -28x + 49x2) = 60

Solving
4 + -28x + 49x2 = 60

Solving for variable 'x'.

Reorder the terms:
4 + -60 + -28x + 49x2 = 60 + -60

Combine like terms: 4 + -60 = -56
-56 + -28x + 49x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-56 + -28x + 49x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + -4x + 7x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-8 + -4x + 7x2)' equal to zero and attempt to solve:

Simplifying
-8 + -4x + 7x2 = 0

Solving
-8 + -4x + 7x2 = 0

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

Divide each side by '7'.
-1.142857143 + -0.5714285714x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -0.5714285714x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -0.5714285714x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -0.5714285714x + x2 = 0 + 1.142857143
-0.5714285714x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-0.5714285714x + x2 = 1.142857143

The x term is -0.5714285714x.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714x + 0.08163265305 + x2 = 1.142857143 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714x + x2 = 1.142857143 + 0.08163265305

Combine like terms: 1.142857143 + 0.08163265305 = 1.22448979605
0.08163265305 + -0.5714285714x + x2 = 1.22448979605

Factor a perfect square on the left side:
(x + -0.2857142857)(x + -0.2857142857) = 1.22448979605

Calculate the square root of the right side: 1.10656667

Break this problem into two subproblems by setting 
(x + -0.2857142857) equal to 1.10656667 and -1.10656667.

Subproblem 1
x + -0.2857142857 = 1.10656667

Simplifying
x + -0.2857142857 = 1.10656667

Reorder the terms:
-0.2857142857 + x = 1.10656667

Solving
-0.2857142857 + x = 1.10656667

Solving for variable 'x'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = 1.10656667 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = 1.10656667 + 0.2857142857
x = 1.10656667 + 0.2857142857

Combine like terms: 1.10656667 + 0.2857142857 = 1.3922809557
x = 1.3922809557

Simplifying
x = 1.3922809557

Subproblem 2
x + -0.2857142857 = -1.10656667

Simplifying
x + -0.2857142857 = -1.10656667

Reorder the terms:
-0.2857142857 + x = -1.10656667

Solving
-0.2857142857 + x = -1.10656667

Solving for variable 'x'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = -1.10656667 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = -1.10656667 + 0.2857142857
x = -1.10656667 + 0.2857142857

Combine like terms: -1.10656667 + 0.2857142857 = -0.8208523843
x = -0.8208523843

Simplifying
x = -0.8208523843

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3922809557, -0.8208523843}
Solution
x = {1.3922809557, -0.8208523843}