13x^2+32x+15=0

Solution for 13x^2+32x+15=0 equation:

Simplifying
13x2 + 32x + 15 = 0

Reorder the terms:
15 + 32x + 13x2 = 0

Solving
15 + 32x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
1.153846154 + 2.461538462x + x2 = 0

Move the constant term to the right:

Add '-1.153846154' to each side of the equation.
1.153846154 + 2.461538462x + -1.153846154 + x2 = 0 + -1.153846154

Reorder the terms:
1.153846154 + -1.153846154 + 2.461538462x + x2 = 0 + -1.153846154

Combine like terms: 1.153846154 + -1.153846154 = 0.000000000
0.000000000 + 2.461538462x + x2 = 0 + -1.153846154
2.461538462x + x2 = 0 + -1.153846154

Combine like terms: 0 + -1.153846154 = -1.153846154
2.461538462x + x2 = -1.153846154

The x term is 2.461538462x.  Take half its coefficient (1.230769231).
Square it (1.514792900) and add it to both sides.

Add '1.514792900' to each side of the equation.
2.461538462x + 1.514792900 + x2 = -1.153846154 + 1.514792900

Reorder the terms:
1.514792900 + 2.461538462x + x2 = -1.153846154 + 1.514792900

Combine like terms: -1.153846154 + 1.514792900 = 0.360946746
1.514792900 + 2.461538462x + x2 = 0.360946746

Factor a perfect square on the left side:
(x + 1.230769231)(x + 1.230769231) = 0.360946746

Calculate the square root of the right side: 0.600788437

Break this problem into two subproblems by setting 
(x + 1.230769231) equal to 0.600788437 and -0.600788437.

Subproblem 1
x + 1.230769231 = 0.600788437

Simplifying
x + 1.230769231 = 0.600788437

Reorder the terms:
1.230769231 + x = 0.600788437

Solving
1.230769231 + x = 0.600788437

Solving for variable 'x'.

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

Add '-1.230769231' to each side of the equation.
1.230769231 + -1.230769231 + x = 0.600788437 + -1.230769231

Combine like terms: 1.230769231 + -1.230769231 = 0.000000000
0.000000000 + x = 0.600788437 + -1.230769231
x = 0.600788437 + -1.230769231

Combine like terms: 0.600788437 + -1.230769231 = -0.629980794
x = -0.629980794

Simplifying
x = -0.629980794

Subproblem 2
x + 1.230769231 = -0.600788437

Simplifying
x + 1.230769231 = -0.600788437

Reorder the terms:
1.230769231 + x = -0.600788437

Solving
1.230769231 + x = -0.600788437

Solving for variable 'x'.

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

Add '-1.230769231' to each side of the equation.
1.230769231 + -1.230769231 + x = -0.600788437 + -1.230769231

Combine like terms: 1.230769231 + -1.230769231 = 0.000000000
0.000000000 + x = -0.600788437 + -1.230769231
x = -0.600788437 + -1.230769231

Combine like terms: -0.600788437 + -1.230769231 = -1.831557668
x = -1.831557668

Simplifying
x = -1.831557668

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.629980794, -1.831557668}