8x^2+29x+1=0

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Solution for 8x^2+29x+1=0 equation: 


Simplifying
8x2 + 29x + 1 = 0

Reorder the terms:
1 + 29x + 8x2 = 0

Solving
1 + 29x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
0.125 + 3.625x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 3.625x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 3.625x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 3.625x + x2 = 0 + -0.125
3.625x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
3.625x + x2 = -0.125

The x term is 3.625x.  Take half its coefficient (1.8125).
Square it (3.28515625) and add it to both sides.

Add '3.28515625' to each side of the equation.
3.625x + 3.28515625 + x2 = -0.125 + 3.28515625

Reorder the terms:
3.28515625 + 3.625x + x2 = -0.125 + 3.28515625

Combine like terms: -0.125 + 3.28515625 = 3.16015625
3.28515625 + 3.625x + x2 = 3.16015625

Factor a perfect square on the left side:
(x + 1.8125)(x + 1.8125) = 3.16015625

Calculate the square root of the right side: 1.777682832

Break this problem into two subproblems by setting 
(x + 1.8125) equal to 1.777682832 and -1.777682832.


Subproblem 1
x + 1.8125 = 1.777682832

Simplifying
x + 1.8125 = 1.777682832

Reorder the terms:
1.8125 + x = 1.777682832

Solving
1.8125 + x = 1.777682832

Solving for variable 'x'.

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

Add '-1.8125' to each side of the equation.
1.8125 + -1.8125 + x = 1.777682832 + -1.8125

Combine like terms: 1.8125 + -1.8125 = 0.0000
0.0000 + x = 1.777682832 + -1.8125
x = 1.777682832 + -1.8125

Combine like terms: 1.777682832 + -1.8125 = -0.034817168
x = -0.034817168

Simplifying
x = -0.034817168


Subproblem 2
x + 1.8125 = -1.777682832

Simplifying
x + 1.8125 = -1.777682832

Reorder the terms:
1.8125 + x = -1.777682832

Solving
1.8125 + x = -1.777682832

Solving for variable 'x'.

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

Add '-1.8125' to each side of the equation.
1.8125 + -1.8125 + x = -1.777682832 + -1.8125

Combine like terms: 1.8125 + -1.8125 = 0.0000
0.0000 + x = -1.777682832 + -1.8125
x = -1.777682832 + -1.8125

Combine like terms: -1.777682832 + -1.8125 = -3.590182832
x = -3.590182832

Simplifying
x = -3.590182832


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.034817168, -3.590182832}

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