16x^2+40x+2=0

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Solution for 16x^2+40x+2=0 equation: 


Simplifying
16x2 + 40x + 2 = 0

Reorder the terms:
2 + 40x + 16x2 = 0

Solving
2 + 40x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 20x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 20x + 8x2)' equal to zero and attempt to solve:

Simplifying
1 + 20x + 8x2 = 0

Solving
1 + 20x + 8x2 = 0

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

Divide each side by '8'.
0.125 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 2.5x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 2.5x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 2.5x + x2 = 0 + -0.125
2.5x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
2.5x + x2 = -0.125

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -0.125 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -0.125 + 1.5625

Combine like terms: -0.125 + 1.5625 = 1.4375
1.5625 + 2.5x + x2 = 1.4375

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 1.4375

Calculate the square root of the right side: 1.198957881

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.198957881 and -1.198957881.


Subproblem 1
x + 1.25 = 1.198957881

Simplifying
x + 1.25 = 1.198957881

Reorder the terms:
1.25 + x = 1.198957881

Solving
1.25 + x = 1.198957881

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.198957881 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.198957881 + -1.25
x = 1.198957881 + -1.25

Combine like terms: 1.198957881 + -1.25 = -0.051042119
x = -0.051042119

Simplifying
x = -0.051042119


Subproblem 2
x + 1.25 = -1.198957881

Simplifying
x + 1.25 = -1.198957881

Reorder the terms:
1.25 + x = -1.198957881

Solving
1.25 + x = -1.198957881

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.198957881 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.198957881 + -1.25
x = -1.198957881 + -1.25

Combine like terms: -1.198957881 + -1.25 = -2.448957881
x = -2.448957881

Simplifying
x = -2.448957881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.051042119, -2.448957881}
Solution
x = {-0.051042119, -2.448957881}

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