10x^2+5x-16=0

Solution for 10x^2+5x-16=0 equation:

Simplifying
10x2 + 5x + -16 = 0

Reorder the terms:
-16 + 5x + 10x2 = 0

Solving
-16 + 5x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-1.6 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.5x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.5x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.5x + x2 = 0 + 1.6
0.5x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.5x + x2 = 1.6

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.6 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.6 + 0.0625

Combine like terms: 1.6 + 0.0625 = 1.6625
0.0625 + 0.5x + x2 = 1.6625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.6625

Calculate the square root of the right side: 1.289379696

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.289379696 and -1.289379696.

Subproblem 1
x + 0.25 = 1.289379696

Simplifying
x + 0.25 = 1.289379696

Reorder the terms:
0.25 + x = 1.289379696

Solving
0.25 + x = 1.289379696

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.289379696 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.289379696 + -0.25
x = 1.289379696 + -0.25

Combine like terms: 1.289379696 + -0.25 = 1.039379696
x = 1.039379696

Simplifying
x = 1.039379696

Subproblem 2
x + 0.25 = -1.289379696

Simplifying
x + 0.25 = -1.289379696

Reorder the terms:
0.25 + x = -1.289379696

Solving
0.25 + x = -1.289379696

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.289379696 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.289379696 + -0.25
x = -1.289379696 + -0.25

Combine like terms: -1.289379696 + -0.25 = -1.539379696
x = -1.539379696

Simplifying
x = -1.539379696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.039379696, -1.539379696}