.15x(2x+1.50)=11.50

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Solution for .15x(2x+1.50)=11.50 equation: 


Simplifying
0.15x(2x + 1.50) = 11.50

Reorder the terms:
0.15x(1.50 + 2x) = 11.50
(1.50 * 0.15x + 2x * 0.15x) = 11.50
(0.225x + 0.3x2) = 11.50

Solving
0.225x + 0.3x2 = 11.50

Solving for variable 'x'.

Reorder the terms:
-11.50 + 0.225x + 0.3x2 = 11.50 + -11.50

Combine like terms: 11.50 + -11.50 = 0.00
-11.50 + 0.225x + 0.3x2 = 0.00

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

Divide each side by '0.3'.
-38.33333333 + 0.75x + x2 = 0.0

Move the constant term to the right:

Add '38.33333333' to each side of the equation.
-38.33333333 + 0.75x + 38.33333333 + x2 = 0.0 + 38.33333333

Reorder the terms:
-38.33333333 + 38.33333333 + 0.75x + x2 = 0.0 + 38.33333333

Combine like terms: -38.33333333 + 38.33333333 = 0.00000000
0.00000000 + 0.75x + x2 = 0.0 + 38.33333333
0.75x + x2 = 0.0 + 38.33333333

Combine like terms: 0.0 + 38.33333333 = 38.33333333
0.75x + x2 = 38.33333333

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 38.33333333 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 38.33333333 + 0.140625

Combine like terms: 38.33333333 + 0.140625 = 38.47395833
0.140625 + 0.75x + x2 = 38.47395833

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 38.47395833

Calculate the square root of the right side: 6.20273797

Break this problem into two subproblems by setting 
(x + 0.375) equal to 6.20273797 and -6.20273797.


Subproblem 1
x + 0.375 = 6.20273797

Simplifying
x + 0.375 = 6.20273797

Reorder the terms:
0.375 + x = 6.20273797

Solving
0.375 + x = 6.20273797

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 6.20273797 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 6.20273797 + -0.375
x = 6.20273797 + -0.375

Combine like terms: 6.20273797 + -0.375 = 5.82773797
x = 5.82773797

Simplifying
x = 5.82773797


Subproblem 2
x + 0.375 = -6.20273797

Simplifying
x + 0.375 = -6.20273797

Reorder the terms:
0.375 + x = -6.20273797

Solving
0.375 + x = -6.20273797

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -6.20273797 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -6.20273797 + -0.375
x = -6.20273797 + -0.375

Combine like terms: -6.20273797 + -0.375 = -6.57773797
x = -6.57773797

Simplifying
x = -6.57773797


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.82773797, -6.57773797}

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