100=3.14(x+1)(x+1)

Solution for 100=3.14(x+1)(x+1) equation:

Simplifying
100 = 3.14(x + 1)(x + 1)

Reorder the terms:
100 = 3.14(1 + x)(x + 1)

Reorder the terms:
100 = 3.14(1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
100 = 3.14(1(1 + x) + x(1 + x))
100 = 3.14((1 * 1 + x * 1) + x(1 + x))
100 = 3.14((1 + 1x) + x(1 + x))
100 = 3.14(1 + 1x + (1 * x + x * x))
100 = 3.14(1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
100 = 3.14(1 + 2x + x2)
100 = (1 * 3.14 + 2x * 3.14 + x2 * 3.14)
100 = (3.14 + 6.28x + 3.14x2)

Solving
100 = 3.14 + 6.28x + 3.14x2

Solving for variable 'x'.

Combine like terms: 100 + -3.14 = 96.86
96.86 + -6.28x + -3.14x2 = 3.14 + 6.28x + 3.14x2 + -3.14 + -6.28x + -3.14x2

Reorder the terms:
96.86 + -6.28x + -3.14x2 = 3.14 + -3.14 + 6.28x + -6.28x + 3.14x2 + -3.14x2

Combine like terms: 3.14 + -3.14 = 0.00
96.86 + -6.28x + -3.14x2 = 0.00 + 6.28x + -6.28x + 3.14x2 + -3.14x2
96.86 + -6.28x + -3.14x2 = 6.28x + -6.28x + 3.14x2 + -3.14x2

Combine like terms: 6.28x + -6.28x = 0.00
96.86 + -6.28x + -3.14x2 = 0.00 + 3.14x2 + -3.14x2
96.86 + -6.28x + -3.14x2 = 3.14x2 + -3.14x2

Combine like terms: 3.14x2 + -3.14x2 = 0.00
96.86 + -6.28x + -3.14x2 = 0.00

Begin completing the square.  Divide all terms by
-3.14 the coefficient of the squared term: 

Divide each side by '-3.14'.
-30.84713376 + 2x + x2 = 0

Move the constant term to the right:

Add '30.84713376' to each side of the equation.
-30.84713376 + 2x + 30.84713376 + x2 = 0 + 30.84713376

Reorder the terms:
-30.84713376 + 30.84713376 + 2x + x2 = 0 + 30.84713376

Combine like terms: -30.84713376 + 30.84713376 = 0.00000000
0.00000000 + 2x + x2 = 0 + 30.84713376
2x + x2 = 0 + 30.84713376

Combine like terms: 0 + 30.84713376 = 30.84713376
2x + x2 = 30.84713376

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 30.84713376 + 1

Reorder the terms:
1 + 2x + x2 = 30.84713376 + 1

Combine like terms: 30.84713376 + 1 = 31.84713376
1 + 2x + x2 = 31.84713376

Factor a perfect square on the left side:
(x + 1)(x + 1) = 31.84713376

Calculate the square root of the right side: 5.64332648

Break this problem into two subproblems by setting 
(x + 1) equal to 5.64332648 and -5.64332648.

Subproblem 1
x + 1 = 5.64332648

Simplifying
x + 1 = 5.64332648

Reorder the terms:
1 + x = 5.64332648

Solving
1 + x = 5.64332648

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.64332648 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.64332648 + -1
x = 5.64332648 + -1

Combine like terms: 5.64332648 + -1 = 4.64332648
x = 4.64332648

Simplifying
x = 4.64332648

Subproblem 2
x + 1 = -5.64332648

Simplifying
x + 1 = -5.64332648

Reorder the terms:
1 + x = -5.64332648

Solving
1 + x = -5.64332648

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.64332648 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.64332648 + -1
x = -5.64332648 + -1

Combine like terms: -5.64332648 + -1 = -6.64332648
x = -6.64332648

Simplifying
x = -6.64332648

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.64332648, -6.64332648}