(8x+22)(8x+22)=75

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Solution for (8x+22)(8x+22)=75 equation: 


Simplifying
(8x + 22)(8x + 22) = 75

Reorder the terms:
(22 + 8x)(8x + 22) = 75

Reorder the terms:
(22 + 8x)(22 + 8x) = 75

Multiply (22 + 8x) * (22 + 8x)
(22(22 + 8x) + 8x * (22 + 8x)) = 75
((22 * 22 + 8x * 22) + 8x * (22 + 8x)) = 75
((484 + 176x) + 8x * (22 + 8x)) = 75
(484 + 176x + (22 * 8x + 8x * 8x)) = 75
(484 + 176x + (176x + 64x2)) = 75

Combine like terms: 176x + 176x = 352x
(484 + 352x + 64x2) = 75

Solving
484 + 352x + 64x2 = 75

Solving for variable 'x'.

Reorder the terms:
484 + -75 + 352x + 64x2 = 75 + -75

Combine like terms: 484 + -75 = 409
409 + 352x + 64x2 = 75 + -75

Combine like terms: 75 + -75 = 0
409 + 352x + 64x2 = 0

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

Divide each side by '64'.
6.390625 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-6.390625' to each side of the equation.
6.390625 + 5.5x + -6.390625 + x2 = 0 + -6.390625

Reorder the terms:
6.390625 + -6.390625 + 5.5x + x2 = 0 + -6.390625

Combine like terms: 6.390625 + -6.390625 = 0.000000
0.000000 + 5.5x + x2 = 0 + -6.390625
5.5x + x2 = 0 + -6.390625

Combine like terms: 0 + -6.390625 = -6.390625
5.5x + x2 = -6.390625

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -6.390625 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -6.390625 + 7.5625

Combine like terms: -6.390625 + 7.5625 = 1.171875
7.5625 + 5.5x + x2 = 1.171875

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 1.171875

Calculate the square root of the right side: 1.082531755

Break this problem into two subproblems by setting 
(x + 2.75) equal to 1.082531755 and -1.082531755.


Subproblem 1
x + 2.75 = 1.082531755

Simplifying
x + 2.75 = 1.082531755

Reorder the terms:
2.75 + x = 1.082531755

Solving
2.75 + x = 1.082531755

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 1.082531755 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 1.082531755 + -2.75
x = 1.082531755 + -2.75

Combine like terms: 1.082531755 + -2.75 = -1.667468245
x = -1.667468245

Simplifying
x = -1.667468245


Subproblem 2
x + 2.75 = -1.082531755

Simplifying
x + 2.75 = -1.082531755

Reorder the terms:
2.75 + x = -1.082531755

Solving
2.75 + x = -1.082531755

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -1.082531755 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -1.082531755 + -2.75
x = -1.082531755 + -2.75

Combine like terms: -1.082531755 + -2.75 = -3.832531755
x = -3.832531755

Simplifying
x = -3.832531755


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.667468245, -3.832531755}

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