13.11+0.08x(x+3)=13.61+0.12

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Solution for 13.11+0.08x(x+3)=13.61+0.12 equation: 


Simplifying
13.11 + 0.08x(x + 3) = 13.61 + 0.12

Reorder the terms:
13.11 + 0.08x(3 + x) = 13.61 + 0.12
13.11 + (3 * 0.08x + x * 0.08x) = 13.61 + 0.12
13.11 + (0.24x + 0.08x2) = 13.61 + 0.12

Combine like terms: 13.61 + 0.12 = 13.73
13.11 + 0.24x + 0.08x2 = 13.73

Solving
13.11 + 0.24x + 0.08x2 = 13.73

Solving for variable 'x'.

Reorder the terms:
13.11 + -13.73 + 0.24x + 0.08x2 = 13.73 + -13.73

Combine like terms: 13.11 + -13.73 = -0.62
-0.62 + 0.24x + 0.08x2 = 13.73 + -13.73

Combine like terms: 13.73 + -13.73 = 0.00
-0.62 + 0.24x + 0.08x2 = 0.00

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

Divide each side by '0.08'.
-7.75 + 3x + x2 = 0

Move the constant term to the right:

Add '7.75' to each side of the equation.
-7.75 + 3x + 7.75 + x2 = 0 + 7.75

Reorder the terms:
-7.75 + 7.75 + 3x + x2 = 0 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + 3x + x2 = 0 + 7.75
3x + x2 = 0 + 7.75

Combine like terms: 0 + 7.75 = 7.75
3x + x2 = 7.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 7.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 7.75 + 2.25

Combine like terms: 7.75 + 2.25 = 10
2.25 + 3x + x2 = 10

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 1.5 = 3.16227766

Simplifying
x + 1.5 = 3.16227766

Reorder the terms:
1.5 + x = 3.16227766

Solving
1.5 + x = 3.16227766

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.16227766 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.16227766 + -1.5
x = 3.16227766 + -1.5

Combine like terms: 3.16227766 + -1.5 = 1.66227766
x = 1.66227766

Simplifying
x = 1.66227766


Subproblem 2
x + 1.5 = -3.16227766

Simplifying
x + 1.5 = -3.16227766

Reorder the terms:
1.5 + x = -3.16227766

Solving
1.5 + x = -3.16227766

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.16227766 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.16227766 + -1.5
x = -3.16227766 + -1.5

Combine like terms: -3.16227766 + -1.5 = -4.66227766
x = -4.66227766

Simplifying
x = -4.66227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.66227766, -4.66227766}

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