15.52+0.07x(x+3)=16.27-0.08x

Solution for 15.52+0.07x(x+3)=16.27-0.08x equation:

Simplifying
15.52 + 0.07x(x + 3) = 16.27 + -0.08x

Reorder the terms:
15.52 + 0.07x(3 + x) = 16.27 + -0.08x
15.52 + (3 * 0.07x + x * 0.07x) = 16.27 + -0.08x
15.52 + (0.21x + 0.07x2) = 16.27 + -0.08x

Solving
15.52 + 0.21x + 0.07x2 = 16.27 + -0.08x

Solving for variable 'x'.

Reorder the terms:
15.52 + -16.27 + 0.21x + 0.08x + 0.07x2 = 16.27 + -0.08x + -16.27 + 0.08x

Combine like terms: 15.52 + -16.27 = -0.75
-0.75 + 0.21x + 0.08x + 0.07x2 = 16.27 + -0.08x + -16.27 + 0.08x

Combine like terms: 0.21x + 0.08x = 0.29x
-0.75 + 0.29x + 0.07x2 = 16.27 + -0.08x + -16.27 + 0.08x

Reorder the terms:
-0.75 + 0.29x + 0.07x2 = 16.27 + -16.27 + -0.08x + 0.08x

Combine like terms: 16.27 + -16.27 = 0.00
-0.75 + 0.29x + 0.07x2 = 0.00 + -0.08x + 0.08x
-0.75 + 0.29x + 0.07x2 = -0.08x + 0.08x

Combine like terms: -0.08x + 0.08x = 0.00
-0.75 + 0.29x + 0.07x2 = 0.00

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

Divide each side by '0.07'.
-10.71428571 + 4.142857143x + x2 = 0

Move the constant term to the right:

Add '10.71428571' to each side of the equation.
-10.71428571 + 4.142857143x + 10.71428571 + x2 = 0 + 10.71428571

Reorder the terms:
-10.71428571 + 10.71428571 + 4.142857143x + x2 = 0 + 10.71428571

Combine like terms: -10.71428571 + 10.71428571 = 0.00000000
0.00000000 + 4.142857143x + x2 = 0 + 10.71428571
4.142857143x + x2 = 0 + 10.71428571

Combine like terms: 0 + 10.71428571 = 10.71428571
4.142857143x + x2 = 10.71428571

The x term is 4.142857143x.  Take half its coefficient (2.071428572).
Square it (4.290816329) and add it to both sides.

Add '4.290816329' to each side of the equation.
4.142857143x + 4.290816329 + x2 = 10.71428571 + 4.290816329

Reorder the terms:
4.290816329 + 4.142857143x + x2 = 10.71428571 + 4.290816329

Combine like terms: 10.71428571 + 4.290816329 = 15.005102039
4.290816329 + 4.142857143x + x2 = 15.005102039

Factor a perfect square on the left side:
(x + 2.071428572)(x + 2.071428572) = 15.005102039

Calculate the square root of the right side: 3.873641961

Break this problem into two subproblems by setting 
(x + 2.071428572) equal to 3.873641961 and -3.873641961.

Subproblem 1
x + 2.071428572 = 3.873641961

Simplifying
x + 2.071428572 = 3.873641961

Reorder the terms:
2.071428572 + x = 3.873641961

Solving
2.071428572 + x = 3.873641961

Solving for variable 'x'.

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

Add '-2.071428572' to each side of the equation.
2.071428572 + -2.071428572 + x = 3.873641961 + -2.071428572

Combine like terms: 2.071428572 + -2.071428572 = 0.000000000
0.000000000 + x = 3.873641961 + -2.071428572
x = 3.873641961 + -2.071428572

Combine like terms: 3.873641961 + -2.071428572 = 1.802213389
x = 1.802213389

Simplifying
x = 1.802213389

Subproblem 2
x + 2.071428572 = -3.873641961

Simplifying
x + 2.071428572 = -3.873641961

Reorder the terms:
2.071428572 + x = -3.873641961

Solving
2.071428572 + x = -3.873641961

Solving for variable 'x'.

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

Add '-2.071428572' to each side of the equation.
2.071428572 + -2.071428572 + x = -3.873641961 + -2.071428572

Combine like terms: 2.071428572 + -2.071428572 = 0.000000000
0.000000000 + x = -3.873641961 + -2.071428572
x = -3.873641961 + -2.071428572

Combine like terms: -3.873641961 + -2.071428572 = -5.945070533
x = -5.945070533

Simplifying
x = -5.945070533

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.802213389, -5.945070533}