0=2x^2+16x-10

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

Simplifying
0 = 2x2 + 16x + -10

Reorder the terms:
0 = -10 + 16x + 2x2

Solving
0 = -10 + 16x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 10 = 10
10 + -16x + -2x2 = -10 + 16x + 2x2 + 10 + -16x + -2x2

Reorder the terms:
10 + -16x + -2x2 = -10 + 10 + 16x + -16x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
10 + -16x + -2x2 = 0 + 16x + -16x + 2x2 + -2x2
10 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2

Combine like terms: 16x + -16x = 0
10 + -16x + -2x2 = 0 + 2x2 + -2x2
10 + -16x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + -16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -8x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -8x + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -8x + -1x2 = 0

Solving
5 + -8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 8x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 8x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 8x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 8x + x2 = 0 + 5
8x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
8x + x2 = 5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 5 + 16

Reorder the terms:
16 + 8x + x2 = 5 + 16

Combine like terms: 5 + 16 = 21
16 + 8x + x2 = 21

Factor a perfect square on the left side:
(x + 4)(x + 4) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + 4) equal to 4.582575695 and -4.582575695.

Subproblem 1
x + 4 = 4.582575695

Simplifying
x + 4 = 4.582575695

Reorder the terms:
4 + x = 4.582575695

Solving
4 + x = 4.582575695

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.582575695 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.582575695 + -4
x = 4.582575695 + -4

Combine like terms: 4.582575695 + -4 = 0.582575695
x = 0.582575695

Simplifying
x = 0.582575695

Subproblem 2
x + 4 = -4.582575695

Simplifying
x + 4 = -4.582575695

Reorder the terms:
4 + x = -4.582575695

Solving
4 + x = -4.582575695

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.582575695 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.582575695 + -4
x = -4.582575695 + -4

Combine like terms: -4.582575695 + -4 = -8.582575695
x = -8.582575695

Simplifying
x = -8.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.582575695, -8.582575695}
Solution
x = {0.582575695, -8.582575695}