8x^2+100x+3=0

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Solution for 8x^2+100x+3=0 equation: 


Simplifying
8x2 + 100x + 3 = 0

Reorder the terms:
3 + 100x + 8x2 = 0

Solving
3 + 100x + 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'.
0.375 + 12.5x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 12.5x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 12.5x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 12.5x + x2 = 0 + -0.375
12.5x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
12.5x + x2 = -0.375

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = -0.375 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = -0.375 + 39.0625

Combine like terms: -0.375 + 39.0625 = 38.6875
39.0625 + 12.5x + x2 = 38.6875

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 38.6875

Calculate the square root of the right side: 6.219927652

Break this problem into two subproblems by setting 
(x + 6.25) equal to 6.219927652 and -6.219927652.


Subproblem 1
x + 6.25 = 6.219927652

Simplifying
x + 6.25 = 6.219927652

Reorder the terms:
6.25 + x = 6.219927652

Solving
6.25 + x = 6.219927652

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = 6.219927652 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 6.219927652 + -6.25
x = 6.219927652 + -6.25

Combine like terms: 6.219927652 + -6.25 = -0.030072348
x = -0.030072348

Simplifying
x = -0.030072348


Subproblem 2
x + 6.25 = -6.219927652

Simplifying
x + 6.25 = -6.219927652

Reorder the terms:
6.25 + x = -6.219927652

Solving
6.25 + x = -6.219927652

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = -6.219927652 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -6.219927652 + -6.25
x = -6.219927652 + -6.25

Combine like terms: -6.219927652 + -6.25 = -12.469927652
x = -12.469927652

Simplifying
x = -12.469927652


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.030072348, -12.469927652}

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