11(4-6x+5)(13x+1)=5

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Solution for 11(4-6x+5)(13x+1)=5 equation:


Simplifying
11(4 + -6x + 5)(13x + 1) = 5

Reorder the terms:
11(4 + 5 + -6x)(13x + 1) = 5

Combine like terms: 4 + 5 = 9
11(9 + -6x)(13x + 1) = 5

Reorder the terms:
11(9 + -6x)(1 + 13x) = 5

Multiply (9 + -6x) * (1 + 13x)
11(9(1 + 13x) + -6x * (1 + 13x)) = 5
11((1 * 9 + 13x * 9) + -6x * (1 + 13x)) = 5
11((9 + 117x) + -6x * (1 + 13x)) = 5
11(9 + 117x + (1 * -6x + 13x * -6x)) = 5
11(9 + 117x + (-6x + -78x2)) = 5

Combine like terms: 117x + -6x = 111x
11(9 + 111x + -78x2) = 5
(9 * 11 + 111x * 11 + -78x2 * 11) = 5
(99 + 1221x + -858x2) = 5

Solving
99 + 1221x + -858x2 = 5

Solving for variable 'x'.

Reorder the terms:
99 + -5 + 1221x + -858x2 = 5 + -5

Combine like terms: 99 + -5 = 94
94 + 1221x + -858x2 = 5 + -5

Combine like terms: 5 + -5 = 0
94 + 1221x + -858x2 = 0

Begin completing the square.  Divide all terms by
-858 the coefficient of the squared term: 

Divide each side by '-858'.
-0.1095571096 + -1.423076923x + x2 = 0

Move the constant term to the right:

Add '0.1095571096' to each side of the equation.
-0.1095571096 + -1.423076923x + 0.1095571096 + x2 = 0 + 0.1095571096

Reorder the terms:
-0.1095571096 + 0.1095571096 + -1.423076923x + x2 = 0 + 0.1095571096

Combine like terms: -0.1095571096 + 0.1095571096 = 0.0000000000
0.0000000000 + -1.423076923x + x2 = 0 + 0.1095571096
-1.423076923x + x2 = 0 + 0.1095571096

Combine like terms: 0 + 0.1095571096 = 0.1095571096
-1.423076923x + x2 = 0.1095571096

The x term is -1.423076923x.  Take half its coefficient (-0.7115384615).
Square it (0.5062869822) and add it to both sides.

Add '0.5062869822' to each side of the equation.
-1.423076923x + 0.5062869822 + x2 = 0.1095571096 + 0.5062869822

Reorder the terms:
0.5062869822 + -1.423076923x + x2 = 0.1095571096 + 0.5062869822

Combine like terms: 0.1095571096 + 0.5062869822 = 0.6158440918
0.5062869822 + -1.423076923x + x2 = 0.6158440918

Factor a perfect square on the left side:
(x + -0.7115384615)(x + -0.7115384615) = 0.6158440918

Calculate the square root of the right side: 0.784757346

Break this problem into two subproblems by setting 
(x + -0.7115384615) equal to 0.784757346 and -0.784757346.

Subproblem 1

x + -0.7115384615 = 0.784757346 Simplifying x + -0.7115384615 = 0.784757346 Reorder the terms: -0.7115384615 + x = 0.784757346 Solving -0.7115384615 + x = 0.784757346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7115384615' to each side of the equation. -0.7115384615 + 0.7115384615 + x = 0.784757346 + 0.7115384615 Combine like terms: -0.7115384615 + 0.7115384615 = 0.0000000000 0.0000000000 + x = 0.784757346 + 0.7115384615 x = 0.784757346 + 0.7115384615 Combine like terms: 0.784757346 + 0.7115384615 = 1.4962958075 x = 1.4962958075 Simplifying x = 1.4962958075

Subproblem 2

x + -0.7115384615 = -0.784757346 Simplifying x + -0.7115384615 = -0.784757346 Reorder the terms: -0.7115384615 + x = -0.784757346 Solving -0.7115384615 + x = -0.784757346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7115384615' to each side of the equation. -0.7115384615 + 0.7115384615 + x = -0.784757346 + 0.7115384615 Combine like terms: -0.7115384615 + 0.7115384615 = 0.0000000000 0.0000000000 + x = -0.784757346 + 0.7115384615 x = -0.784757346 + 0.7115384615 Combine like terms: -0.784757346 + 0.7115384615 = -0.0732188845 x = -0.0732188845 Simplifying x = -0.0732188845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4962958075, -0.0732188845}

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