133=(2x+1)(x+1)

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Solution for 133=(2x+1)(x+1) equation:


Simplifying
133 = (2x + 1)(x + 1)

Reorder the terms:
133 = (1 + 2x)(x + 1)

Reorder the terms:
133 = (1 + 2x)(1 + x)

Multiply (1 + 2x) * (1 + x)
133 = (1(1 + x) + 2x * (1 + x))
133 = ((1 * 1 + x * 1) + 2x * (1 + x))
133 = ((1 + 1x) + 2x * (1 + x))
133 = (1 + 1x + (1 * 2x + x * 2x))
133 = (1 + 1x + (2x + 2x2))

Combine like terms: 1x + 2x = 3x
133 = (1 + 3x + 2x2)

Solving
133 = 1 + 3x + 2x2

Solving for variable 'x'.

Combine like terms: 133 + -1 = 132
132 + -3x + -2x2 = 1 + 3x + 2x2 + -1 + -3x + -2x2

Reorder the terms:
132 + -3x + -2x2 = 1 + -1 + 3x + -3x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
132 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
132 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
132 + -3x + -2x2 = 0 + 2x2 + -2x2
132 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
132 + -3x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-66 + 1.5x + x2 = 0

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 1.5x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + 1.5x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 1.5x + x2 = 0 + 66
1.5x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
1.5x + x2 = 66

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 66 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 66 + 0.5625

Combine like terms: 66 + 0.5625 = 66.5625
0.5625 + 1.5x + x2 = 66.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 66.5625

Calculate the square root of the right side: 8.158584436

Break this problem into two subproblems by setting 
(x + 0.75) equal to 8.158584436 and -8.158584436.

Subproblem 1

x + 0.75 = 8.158584436 Simplifying x + 0.75 = 8.158584436 Reorder the terms: 0.75 + x = 8.158584436 Solving 0.75 + x = 8.158584436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 8.158584436 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 8.158584436 + -0.75 x = 8.158584436 + -0.75 Combine like terms: 8.158584436 + -0.75 = 7.408584436 x = 7.408584436 Simplifying x = 7.408584436

Subproblem 2

x + 0.75 = -8.158584436 Simplifying x + 0.75 = -8.158584436 Reorder the terms: 0.75 + x = -8.158584436 Solving 0.75 + x = -8.158584436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -8.158584436 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -8.158584436 + -0.75 x = -8.158584436 + -0.75 Combine like terms: -8.158584436 + -0.75 = -8.908584436 x = -8.908584436 Simplifying x = -8.908584436

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.408584436, -8.908584436}

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