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

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


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

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

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

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

Combine like terms: 7x + -1x = 6x
(-7 + 6x + x2) = (x + 1) * 2

Reorder the terms:
-7 + 6x + x2 = (1 + x) * 2

Reorder the terms for easier multiplication:
-7 + 6x + x2 = 2(1 + x)
-7 + 6x + x2 = (1 * 2 + x * 2)
-7 + 6x + x2 = (2 + 2x)

Solving
-7 + 6x + x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
-7 + -2 + 6x + -2x + x2 = 2 + 2x + -2 + -2x

Combine like terms: -7 + -2 = -9
-9 + 6x + -2x + x2 = 2 + 2x + -2 + -2x

Combine like terms: 6x + -2x = 4x
-9 + 4x + x2 = 2 + 2x + -2 + -2x

Reorder the terms:
-9 + 4x + x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
-9 + 4x + x2 = 0 + 2x + -2x
-9 + 4x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-9 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 4x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 4x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 4x + x2 = 0 + 9
4x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
4x + x2 = 9

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 9 + 4

Reorder the terms:
4 + 4x + x2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + 4x + x2 = 13

Factor a perfect square on the left side:
(x + 2)(x + 2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 2) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + 2 = 3.605551275 Simplifying x + 2 = 3.605551275 Reorder the terms: 2 + x = 3.605551275 Solving 2 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.605551275 + -2 x = 3.605551275 + -2 Combine like terms: 3.605551275 + -2 = 1.605551275 x = 1.605551275 Simplifying x = 1.605551275

Subproblem 2

x + 2 = -3.605551275 Simplifying x + 2 = -3.605551275 Reorder the terms: 2 + x = -3.605551275 Solving 2 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.605551275 + -2 x = -3.605551275 + -2 Combine like terms: -3.605551275 + -2 = -5.605551275 x = -5.605551275 Simplifying x = -5.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.605551275, -5.605551275}

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