(7x-8)(7x-8)=13

Solution for (7x-8)(7x-8)=13 equation:

Simplifying
(7x + -8)(7x + -8) = 13

Reorder the terms:
(-8 + 7x)(7x + -8) = 13

Reorder the terms:
(-8 + 7x)(-8 + 7x) = 13

Multiply (-8 + 7x) * (-8 + 7x)
(-8(-8 + 7x) + 7x * (-8 + 7x)) = 13
((-8 * -8 + 7x * -8) + 7x * (-8 + 7x)) = 13
((64 + -56x) + 7x * (-8 + 7x)) = 13
(64 + -56x + (-8 * 7x + 7x * 7x)) = 13
(64 + -56x + (-56x + 49x2)) = 13

Combine like terms: -56x + -56x = -112x
(64 + -112x + 49x2) = 13

Solving
64 + -112x + 49x2 = 13

Solving for variable 'x'.

Reorder the terms:
64 + -13 + -112x + 49x2 = 13 + -13

Combine like terms: 64 + -13 = 51
51 + -112x + 49x2 = 13 + -13

Combine like terms: 13 + -13 = 0
51 + -112x + 49x2 = 0

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

Divide each side by '49'.
1.040816327 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '-1.040816327' to each side of the equation.
1.040816327 + -2.285714286x + -1.040816327 + x2 = 0 + -1.040816327

Reorder the terms:
1.040816327 + -1.040816327 + -2.285714286x + x2 = 0 + -1.040816327

Combine like terms: 1.040816327 + -1.040816327 = 0.000000000
0.000000000 + -2.285714286x + x2 = 0 + -1.040816327
-2.285714286x + x2 = 0 + -1.040816327

Combine like terms: 0 + -1.040816327 = -1.040816327
-2.285714286x + x2 = -1.040816327

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = -1.040816327 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = -1.040816327 + 1.306122449

Combine like terms: -1.040816327 + 1.306122449 = 0.265306122
1.306122449 + -2.285714286x + x2 = 0.265306122

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 0.265306122

Calculate the square root of the right side: 0.515078753

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 0.515078753 and -0.515078753.

Subproblem 1
x + -1.142857143 = 0.515078753

Simplifying
x + -1.142857143 = 0.515078753

Reorder the terms:
-1.142857143 + x = 0.515078753

Solving
-1.142857143 + x = 0.515078753

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = 0.515078753 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = 0.515078753 + 1.142857143
x = 0.515078753 + 1.142857143

Combine like terms: 0.515078753 + 1.142857143 = 1.657935896
x = 1.657935896

Simplifying
x = 1.657935896

Subproblem 2
x + -1.142857143 = -0.515078753

Simplifying
x + -1.142857143 = -0.515078753

Reorder the terms:
-1.142857143 + x = -0.515078753

Solving
-1.142857143 + x = -0.515078753

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = -0.515078753 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = -0.515078753 + 1.142857143
x = -0.515078753 + 1.142857143

Combine like terms: -0.515078753 + 1.142857143 = 0.62777839
x = 0.62777839

Simplifying
x = 0.62777839

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.657935896, 0.62777839}