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

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

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

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

Reorder the terms for easier multiplication:
2(1 + x) + -2x(x + -7) = 0
(1 * 2 + x * 2) + -2x(x + -7) = 0
(2 + 2x) + -2x(x + -7) = 0

Reorder the terms:
2 + 2x + -2x(-7 + x) = 0
2 + 2x + (-7 * -2x + x * -2x) = 0
2 + 2x + (14x + -2x2) = 0

Combine like terms: 2x + 14x = 16x
2 + 16x + -2x2 = 0

Solving
2 + 16x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 8x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
1 + 8x + -1x2 = 0

Solving
1 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -8x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -8x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -8x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x + x2 = 0 + 1
-8x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-8x + x2 = 1

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 1 + 16

Reorder the terms:
16 + -8x + x2 = 1 + 16

Combine like terms: 1 + 16 = 17
16 + -8x + x2 = 17

Factor a perfect square on the left side:
(x + -4)(x + -4) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -4) equal to 4.123105626 and -4.123105626.

Subproblem 1
x + -4 = 4.123105626

Simplifying
x + -4 = 4.123105626

Reorder the terms:
-4 + x = 4.123105626

Solving
-4 + x = 4.123105626

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.123105626 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.123105626 + 4
x = 4.123105626 + 4

Combine like terms: 4.123105626 + 4 = 8.123105626
x = 8.123105626

Simplifying
x = 8.123105626

Subproblem 2
x + -4 = -4.123105626

Simplifying
x + -4 = -4.123105626

Reorder the terms:
-4 + x = -4.123105626

Solving
-4 + x = -4.123105626

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.123105626 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.123105626 + 4
x = -4.123105626 + 4

Combine like terms: -4.123105626 + 4 = -0.123105626
x = -0.123105626

Simplifying
x = -0.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.123105626, -0.123105626}
Solution
x = {8.123105626, -0.123105626}