16x^2+40x+5=0

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Solution for 16x^2+40x+5=0 equation:


Simplifying
16x2 + 40x + 5 = 0

Reorder the terms:
5 + 40x + 16x2 = 0

Solving
5 + 40x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
0.3125 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + 2.5x + -0.3125 + x2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + 2.5x + x2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + 2.5x + x2 = 0 + -0.3125
2.5x + x2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
2.5x + x2 = -0.3125

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 = -0.3125 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -0.3125 + 1.5625

Combine like terms: -0.3125 + 1.5625 = 1.25
1.5625 + 2.5x + x2 = 1.25

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

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 1.25 = 1.118033989 Simplifying x + 1.25 = 1.118033989 Reorder the terms: 1.25 + x = 1.118033989 Solving 1.25 + x = 1.118033989 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 = 1.118033989 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.118033989 + -1.25 x = 1.118033989 + -1.25 Combine like terms: 1.118033989 + -1.25 = -0.131966011 x = -0.131966011 Simplifying x = -0.131966011

Subproblem 2

x + 1.25 = -1.118033989 Simplifying x + 1.25 = -1.118033989 Reorder the terms: 1.25 + x = -1.118033989 Solving 1.25 + x = -1.118033989 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 = -1.118033989 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.118033989 + -1.25 x = -1.118033989 + -1.25 Combine like terms: -1.118033989 + -1.25 = -2.368033989 x = -2.368033989 Simplifying x = -2.368033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.131966011, -2.368033989}

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