(6x)(12x+5)=77

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Solution for (6x)(12x+5)=77 equation:


Simplifying
(6x)(12x + 5) = 77

Remove parenthesis around (6x)
6x(12x + 5) = 77

Reorder the terms:
6x(5 + 12x) = 77
(5 * 6x + 12x * 6x) = 77
(30x + 72x2) = 77

Solving
30x + 72x2 = 77

Solving for variable 'x'.

Reorder the terms:
-77 + 30x + 72x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 30x + 72x2 = 0

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

Divide each side by '72'.
-1.069444444 + 0.4166666667x + x2 = 0

Move the constant term to the right:

Add '1.069444444' to each side of the equation.
-1.069444444 + 0.4166666667x + 1.069444444 + x2 = 0 + 1.069444444

Reorder the terms:
-1.069444444 + 1.069444444 + 0.4166666667x + x2 = 0 + 1.069444444

Combine like terms: -1.069444444 + 1.069444444 = 0.000000000
0.000000000 + 0.4166666667x + x2 = 0 + 1.069444444
0.4166666667x + x2 = 0 + 1.069444444

Combine like terms: 0 + 1.069444444 = 1.069444444
0.4166666667x + x2 = 1.069444444

The x term is 0.4166666667x.  Take half its coefficient (0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
0.4166666667x + 0.04340277781 + x2 = 1.069444444 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667x + x2 = 1.069444444 + 0.04340277781

Combine like terms: 1.069444444 + 0.04340277781 = 1.11284722181
0.04340277781 + 0.4166666667x + x2 = 1.11284722181

Factor a perfect square on the left side:
(x + 0.2083333334)(x + 0.2083333334) = 1.11284722181

Calculate the square root of the right side: 1.054915742

Break this problem into two subproblems by setting 
(x + 0.2083333334) equal to 1.054915742 and -1.054915742.

Subproblem 1

x + 0.2083333334 = 1.054915742 Simplifying x + 0.2083333334 = 1.054915742 Reorder the terms: 0.2083333334 + x = 1.054915742 Solving 0.2083333334 + x = 1.054915742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 1.054915742 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 1.054915742 + -0.2083333334 x = 1.054915742 + -0.2083333334 Combine like terms: 1.054915742 + -0.2083333334 = 0.8465824086 x = 0.8465824086 Simplifying x = 0.8465824086

Subproblem 2

x + 0.2083333334 = -1.054915742 Simplifying x + 0.2083333334 = -1.054915742 Reorder the terms: 0.2083333334 + x = -1.054915742 Solving 0.2083333334 + x = -1.054915742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -1.054915742 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -1.054915742 + -0.2083333334 x = -1.054915742 + -0.2083333334 Combine like terms: -1.054915742 + -0.2083333334 = -1.2632490754 x = -1.2632490754 Simplifying x = -1.2632490754

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8465824086, -1.2632490754}

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