5x(6x+9)=11

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Solution for 5x(6x+9)=11 equation: 


Simplifying
5x(6x + 9) = 11

Reorder the terms:
5x(9 + 6x) = 11
(9 * 5x + 6x * 5x) = 11
(45x + 30x2) = 11

Solving
45x + 30x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + 45x + 30x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 45x + 30x2 = 0

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

Divide each side by '30'.
-0.3666666667 + 1.5x + x2 = 0.0

Move the constant term to the right:

Add '0.3666666667' to each side of the equation.
-0.3666666667 + 1.5x + 0.3666666667 + x2 = 0.0 + 0.3666666667

Reorder the terms:
-0.3666666667 + 0.3666666667 + 1.5x + x2 = 0.0 + 0.3666666667

Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000
0.0000000000 + 1.5x + x2 = 0.0 + 0.3666666667
1.5x + x2 = 0.0 + 0.3666666667

Combine like terms: 0.0 + 0.3666666667 = 0.3666666667
1.5x + x2 = 0.3666666667

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 = 0.3666666667 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 0.3666666667 + 0.5625

Combine like terms: 0.3666666667 + 0.5625 = 0.9291666667
0.5625 + 1.5x + x2 = 0.9291666667

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.9291666667

Calculate the square root of the right side: 0.963932916

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.963932916 and -0.963932916.


Subproblem 1
x + 0.75 = 0.963932916

Simplifying
x + 0.75 = 0.963932916

Reorder the terms:
0.75 + x = 0.963932916

Solving
0.75 + x = 0.963932916

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 = 0.963932916 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.963932916 + -0.75
x = 0.963932916 + -0.75

Combine like terms: 0.963932916 + -0.75 = 0.213932916
x = 0.213932916

Simplifying
x = 0.213932916


Subproblem 2
x + 0.75 = -0.963932916

Simplifying
x + 0.75 = -0.963932916

Reorder the terms:
0.75 + x = -0.963932916

Solving
0.75 + x = -0.963932916

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 = -0.963932916 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.963932916 + -0.75
x = -0.963932916 + -0.75

Combine like terms: -0.963932916 + -0.75 = -1.713932916
x = -1.713932916

Simplifying
x = -1.713932916


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.213932916, -1.713932916}

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