(x+1)(x-1)-3x=7

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Solution for (x+1)(x-1)-3x=7 equation: 


Simplifying
(x + 1)(x + -1) + -3x = 7

Reorder the terms:
(1 + x)(x + -1) + -3x = 7

Reorder the terms:
(1 + x)(-1 + x) + -3x = 7

Multiply (1 + x) * (-1 + x)
(1(-1 + x) + x(-1 + x)) + -3x = 7
((-1 * 1 + x * 1) + x(-1 + x)) + -3x = 7
((-1 + 1x) + x(-1 + x)) + -3x = 7
(-1 + 1x + (-1 * x + x * x)) + -3x = 7
(-1 + 1x + (-1x + x2)) + -3x = 7

Combine like terms: 1x + -1x = 0
(-1 + 0 + x2) + -3x = 7
(-1 + x2) + -3x = 7

Reorder the terms:
-1 + -3x + x2 = 7

Solving
-1 + -3x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-1 + -7 + -3x + x2 = 7 + -7

Combine like terms: -1 + -7 = -8
-8 + -3x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-8 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -3x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x + x2 = 0 + 8
-3x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-3x + x2 = 8

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 8 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + -3x + x2 = 10.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + -1.5 = 3.201562119

Simplifying
x + -1.5 = 3.201562119

Reorder the terms:
-1.5 + x = 3.201562119

Solving
-1.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.201562119 + 1.5
x = 3.201562119 + 1.5

Combine like terms: 3.201562119 + 1.5 = 4.701562119
x = 4.701562119

Simplifying
x = 4.701562119


Subproblem 2
x + -1.5 = -3.201562119

Simplifying
x + -1.5 = -3.201562119

Reorder the terms:
-1.5 + x = -3.201562119

Solving
-1.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.201562119 + 1.5
x = -3.201562119 + 1.5

Combine like terms: -3.201562119 + 1.5 = -1.701562119
x = -1.701562119

Simplifying
x = -1.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.701562119, -1.701562119}

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