(8x+5)(8x+5)=63

Solution for (8x+5)(8x+5)=63 equation:

Simplifying
(8x + 5)(8x + 5) = 63

Reorder the terms:
(5 + 8x)(8x + 5) = 63

Reorder the terms:
(5 + 8x)(5 + 8x) = 63

Multiply (5 + 8x) * (5 + 8x)
(5(5 + 8x) + 8x * (5 + 8x)) = 63
((5 * 5 + 8x * 5) + 8x * (5 + 8x)) = 63
((25 + 40x) + 8x * (5 + 8x)) = 63
(25 + 40x + (5 * 8x + 8x * 8x)) = 63
(25 + 40x + (40x + 64x2)) = 63

Combine like terms: 40x + 40x = 80x
(25 + 80x + 64x2) = 63

Solving
25 + 80x + 64x2 = 63

Solving for variable 'x'.

Reorder the terms:
25 + -63 + 80x + 64x2 = 63 + -63

Combine like terms: 25 + -63 = -38
-38 + 80x + 64x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-38 + 80x + 64x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 40x + 32x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + 40x + 32x2)' equal to zero and attempt to solve:

Simplifying
-19 + 40x + 32x2 = 0

Solving
-19 + 40x + 32x2 = 0

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

Divide each side by '32'.
-0.59375 + 1.25x + x2 = 0

Move the constant term to the right:

Add '0.59375' to each side of the equation.
-0.59375 + 1.25x + 0.59375 + x2 = 0 + 0.59375

Reorder the terms:
-0.59375 + 0.59375 + 1.25x + x2 = 0 + 0.59375

Combine like terms: -0.59375 + 0.59375 = 0.00000
0.00000 + 1.25x + x2 = 0 + 0.59375
1.25x + x2 = 0 + 0.59375

Combine like terms: 0 + 0.59375 = 0.59375
1.25x + x2 = 0.59375

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 0.59375 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 0.59375 + 0.390625

Combine like terms: 0.59375 + 0.390625 = 0.984375
0.390625 + 1.25x + x2 = 0.984375

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 0.984375

Calculate the square root of the right side: 0.992156742

Break this problem into two subproblems by setting 
(x + 0.625) equal to 0.992156742 and -0.992156742.

Subproblem 1
x + 0.625 = 0.992156742

Simplifying
x + 0.625 = 0.992156742

Reorder the terms:
0.625 + x = 0.992156742

Solving
0.625 + x = 0.992156742

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 0.992156742 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 0.992156742 + -0.625
x = 0.992156742 + -0.625

Combine like terms: 0.992156742 + -0.625 = 0.367156742
x = 0.367156742

Simplifying
x = 0.367156742

Subproblem 2
x + 0.625 = -0.992156742

Simplifying
x + 0.625 = -0.992156742

Reorder the terms:
0.625 + x = -0.992156742

Solving
0.625 + x = -0.992156742

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -0.992156742 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -0.992156742 + -0.625
x = -0.992156742 + -0.625

Combine like terms: -0.992156742 + -0.625 = -1.617156742
x = -1.617156742

Simplifying
x = -1.617156742

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.367156742, -1.617156742}
Solution
x = {0.367156742, -1.617156742}