(x-1)*(x-1)-(2x+7)*(2x-7)=0

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Solution for (x-1)*(x-1)-(2x+7)*(2x-7)=0 equation: 


Simplifying
(x + -1)(x + -1) + -1(2x + 7)(2x + -7) = 0

Reorder the terms:
(-1 + x)(x + -1) + -1(2x + 7)(2x + -7) = 0

Reorder the terms:
(-1 + x)(-1 + x) + -1(2x + 7)(2x + -7) = 0

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) + -1(2x + 7)(2x + -7) = 0
((-1 * -1 + x * -1) + x(-1 + x)) + -1(2x + 7)(2x + -7) = 0
((1 + -1x) + x(-1 + x)) + -1(2x + 7)(2x + -7) = 0
(1 + -1x + (-1 * x + x * x)) + -1(2x + 7)(2x + -7) = 0
(1 + -1x + (-1x + x2)) + -1(2x + 7)(2x + -7) = 0

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) + -1(2x + 7)(2x + -7) = 0

Reorder the terms:
1 + -2x + x2 + -1(7 + 2x)(2x + -7) = 0

Reorder the terms:
1 + -2x + x2 + -1(7 + 2x)(-7 + 2x) = 0

Multiply (7 + 2x) * (-7 + 2x)
1 + -2x + x2 + -1(7(-7 + 2x) + 2x * (-7 + 2x)) = 0
1 + -2x + x2 + -1((-7 * 7 + 2x * 7) + 2x * (-7 + 2x)) = 0
1 + -2x + x2 + -1((-49 + 14x) + 2x * (-7 + 2x)) = 0
1 + -2x + x2 + -1(-49 + 14x + (-7 * 2x + 2x * 2x)) = 0
1 + -2x + x2 + -1(-49 + 14x + (-14x + 4x2)) = 0

Combine like terms: 14x + -14x = 0
1 + -2x + x2 + -1(-49 + 0 + 4x2) = 0
1 + -2x + x2 + -1(-49 + 4x2) = 0
1 + -2x + x2 + (-49 * -1 + 4x2 * -1) = 0
1 + -2x + x2 + (49 + -4x2) = 0

Reorder the terms:
1 + 49 + -2x + x2 + -4x2 = 0

Combine like terms: 1 + 49 = 50
50 + -2x + x2 + -4x2 = 0

Combine like terms: x2 + -4x2 = -3x2
50 + -2x + -3x2 = 0

Solving
50 + -2x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-16.66666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + 0.6666666667x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + 0.6666666667x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + 0.6666666667x + x2 = 0 + 16.66666667
0.6666666667x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
0.6666666667x + x2 = 16.66666667

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 16.66666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 16.66666667 + 0.1111111112

Combine like terms: 16.66666667 + 0.1111111112 = 16.7777777812
0.1111111112 + 0.6666666667x + x2 = 16.7777777812

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 16.7777777812

Calculate the square root of the right side: 4.096068576

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 4.096068576 and -4.096068576.


Subproblem 1
x + 0.3333333334 = 4.096068576

Simplifying
x + 0.3333333334 = 4.096068576

Reorder the terms:
0.3333333334 + x = 4.096068576

Solving
0.3333333334 + x = 4.096068576

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 4.096068576 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 4.096068576 + -0.3333333334
x = 4.096068576 + -0.3333333334

Combine like terms: 4.096068576 + -0.3333333334 = 3.7627352426
x = 3.7627352426

Simplifying
x = 3.7627352426


Subproblem 2
x + 0.3333333334 = -4.096068576

Simplifying
x + 0.3333333334 = -4.096068576

Reorder the terms:
0.3333333334 + x = -4.096068576

Solving
0.3333333334 + x = -4.096068576

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -4.096068576 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -4.096068576 + -0.3333333334
x = -4.096068576 + -0.3333333334

Combine like terms: -4.096068576 + -0.3333333334 = -4.4294019094
x = -4.4294019094

Simplifying
x = -4.4294019094


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.7627352426, -4.4294019094}

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