(x+1)*(x+1)-2.5x-35.5=0

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Solution for (x+1)*(x+1)-2.5x-35.5=0 equation:


Simplifying
(x + 1)(x + 1) + -2.5x + -35.5 = 0

Reorder the terms:
(1 + x)(x + 1) + -2.5x + -35.5 = 0

Reorder the terms:
(1 + x)(1 + x) + -2.5x + -35.5 = 0

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) + -2.5x + -35.5 = 0
((1 * 1 + x * 1) + x(1 + x)) + -2.5x + -35.5 = 0
((1 + 1x) + x(1 + x)) + -2.5x + -35.5 = 0
(1 + 1x + (1 * x + x * x)) + -2.5x + -35.5 = 0
(1 + 1x + (1x + x2)) + -2.5x + -35.5 = 0

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + -2.5x + -35.5 = 0

Reorder the terms:
1 + -35.5 + 2x + -2.5x + x2 = 0

Combine like terms: 1 + -35.5 = -34.5
-34.5 + 2x + -2.5x + x2 = 0

Combine like terms: 2x + -2.5x = -0.5x
-34.5 + -0.5x + x2 = 0

Solving
-34.5 + -0.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '34.5' to each side of the equation.
-34.5 + -0.5x + 34.5 + x2 = 0 + 34.5

Reorder the terms:
-34.5 + 34.5 + -0.5x + x2 = 0 + 34.5

Combine like terms: -34.5 + 34.5 = 0.0
0.0 + -0.5x + x2 = 0 + 34.5
-0.5x + x2 = 0 + 34.5

Combine like terms: 0 + 34.5 = 34.5
-0.5x + x2 = 34.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 34.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 34.5 + 0.0625

Combine like terms: 34.5 + 0.0625 = 34.5625
0.0625 + -0.5x + x2 = 34.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 34.5625

Calculate the square root of the right side: 5.878988008

Break this problem into two subproblems by setting 
(x + -0.25) equal to 5.878988008 and -5.878988008.

Subproblem 1

x + -0.25 = 5.878988008 Simplifying x + -0.25 = 5.878988008 Reorder the terms: -0.25 + x = 5.878988008 Solving -0.25 + x = 5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 5.878988008 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.878988008 + 0.25 x = 5.878988008 + 0.25 Combine like terms: 5.878988008 + 0.25 = 6.128988008 x = 6.128988008 Simplifying x = 6.128988008

Subproblem 2

x + -0.25 = -5.878988008 Simplifying x + -0.25 = -5.878988008 Reorder the terms: -0.25 + x = -5.878988008 Solving -0.25 + x = -5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -5.878988008 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.878988008 + 0.25 x = -5.878988008 + 0.25 Combine like terms: -5.878988008 + 0.25 = -5.628988008 x = -5.628988008 Simplifying x = -5.628988008

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.128988008, -5.628988008}

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