8x^2+15x+1=0

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Solution for 8x^2+15x+1=0 equation: 


Simplifying
8x2 + 15x + 1 = 0

Reorder the terms:
1 + 15x + 8x2 = 0

Solving
1 + 15x + 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 + 1.875x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 1.875x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 1.875x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 1.875x + x2 = 0 + -0.125
1.875x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
1.875x + x2 = -0.125

The x term is 1.875x.  Take half its coefficient (0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
1.875x + 0.87890625 + x2 = -0.125 + 0.87890625

Reorder the terms:
0.87890625 + 1.875x + x2 = -0.125 + 0.87890625

Combine like terms: -0.125 + 0.87890625 = 0.75390625
0.87890625 + 1.875x + x2 = 0.75390625

Factor a perfect square on the left side:
(x + 0.9375)(x + 0.9375) = 0.75390625

Calculate the square root of the right side: 0.868277749

Break this problem into two subproblems by setting 
(x + 0.9375) equal to 0.868277749 and -0.868277749.


Subproblem 1
x + 0.9375 = 0.868277749

Simplifying
x + 0.9375 = 0.868277749

Reorder the terms:
0.9375 + x = 0.868277749

Solving
0.9375 + x = 0.868277749

Solving for variable 'x'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + x = 0.868277749 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + x = 0.868277749 + -0.9375
x = 0.868277749 + -0.9375

Combine like terms: 0.868277749 + -0.9375 = -0.069222251
x = -0.069222251

Simplifying
x = -0.069222251


Subproblem 2
x + 0.9375 = -0.868277749

Simplifying
x + 0.9375 = -0.868277749

Reorder the terms:
0.9375 + x = -0.868277749

Solving
0.9375 + x = -0.868277749

Solving for variable 'x'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + x = -0.868277749 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + x = -0.868277749 + -0.9375
x = -0.868277749 + -0.9375

Combine like terms: -0.868277749 + -0.9375 = -1.805777749
x = -1.805777749

Simplifying
x = -1.805777749


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.069222251, -1.805777749}

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