(3x+1)(x+1)=266

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Solution for (3x+1)(x+1)=266 equation:


Simplifying
(3x + 1)(x + 1) = 266

Reorder the terms:
(1 + 3x)(x + 1) = 266

Reorder the terms:
(1 + 3x)(1 + x) = 266

Multiply (1 + 3x) * (1 + x)
(1(1 + x) + 3x * (1 + x)) = 266
((1 * 1 + x * 1) + 3x * (1 + x)) = 266
((1 + 1x) + 3x * (1 + x)) = 266
(1 + 1x + (1 * 3x + x * 3x)) = 266
(1 + 1x + (3x + 3x2)) = 266

Combine like terms: 1x + 3x = 4x
(1 + 4x + 3x2) = 266

Solving
1 + 4x + 3x2 = 266

Solving for variable 'x'.

Reorder the terms:
1 + -266 + 4x + 3x2 = 266 + -266

Combine like terms: 1 + -266 = -265
-265 + 4x + 3x2 = 266 + -266

Combine like terms: 266 + -266 = 0
-265 + 4x + 3x2 = 0

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

Divide each side by '3'.
-88.33333333 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '88.33333333' to each side of the equation.
-88.33333333 + 1.333333333x + 88.33333333 + x2 = 0 + 88.33333333

Reorder the terms:
-88.33333333 + 88.33333333 + 1.333333333x + x2 = 0 + 88.33333333

Combine like terms: -88.33333333 + 88.33333333 = 0.00000000
0.00000000 + 1.333333333x + x2 = 0 + 88.33333333
1.333333333x + x2 = 0 + 88.33333333

Combine like terms: 0 + 88.33333333 = 88.33333333
1.333333333x + x2 = 88.33333333

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 88.33333333 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 88.33333333 + 0.4444444442

Combine like terms: 88.33333333 + 0.4444444442 = 88.7777777742
0.4444444442 + 1.333333333x + x2 = 88.7777777742

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 88.7777777742

Calculate the square root of the right side: 9.422196017

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 9.422196017 and -9.422196017.

Subproblem 1

x + 0.6666666665 = 9.422196017 Simplifying x + 0.6666666665 = 9.422196017 Reorder the terms: 0.6666666665 + x = 9.422196017 Solving 0.6666666665 + x = 9.422196017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 9.422196017 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 9.422196017 + -0.6666666665 x = 9.422196017 + -0.6666666665 Combine like terms: 9.422196017 + -0.6666666665 = 8.7555293505 x = 8.7555293505 Simplifying x = 8.7555293505

Subproblem 2

x + 0.6666666665 = -9.422196017 Simplifying x + 0.6666666665 = -9.422196017 Reorder the terms: 0.6666666665 + x = -9.422196017 Solving 0.6666666665 + x = -9.422196017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -9.422196017 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -9.422196017 + -0.6666666665 x = -9.422196017 + -0.6666666665 Combine like terms: -9.422196017 + -0.6666666665 = -10.0888626835 x = -10.0888626835 Simplifying x = -10.0888626835

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.7555293505, -10.0888626835}

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