6x^2+2.5x+0.25=0

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Solution for 6x^2+2.5x+0.25=0 equation: 


Simplifying
6x2 + 2.5x + 0.25 = 0

Reorder the terms:
0.25 + 2.5x + 6x2 = 0

Solving
0.25 + 2.5x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
0.04166666667 + 0.4166666667x + x2 = 0

Move the constant term to the right:

Add '-0.04166666667' to each side of the equation.
0.04166666667 + 0.4166666667x + -0.04166666667 + x2 = 0 + -0.04166666667

Reorder the terms:
0.04166666667 + -0.04166666667 + 0.4166666667x + x2 = 0 + -0.04166666667

Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000
0.00000000000 + 0.4166666667x + x2 = 0 + -0.04166666667
0.4166666667x + x2 = 0 + -0.04166666667

Combine like terms: 0 + -0.04166666667 = -0.04166666667
0.4166666667x + x2 = -0.04166666667

The x term is 0.4166666667x.  Take half its coefficient (0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
0.4166666667x + 0.04340277781 + x2 = -0.04166666667 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667x + x2 = -0.04166666667 + 0.04340277781

Combine like terms: -0.04166666667 + 0.04340277781 = 0.00173611114
0.04340277781 + 0.4166666667x + x2 = 0.00173611114

Factor a perfect square on the left side:
(x + 0.2083333334)(x + 0.2083333334) = 0.00173611114

Calculate the square root of the right side: 0.041666667

Break this problem into two subproblems by setting 
(x + 0.2083333334) equal to 0.041666667 and -0.041666667.


Subproblem 1
x + 0.2083333334 = 0.041666667

Simplifying
x + 0.2083333334 = 0.041666667

Reorder the terms:
0.2083333334 + x = 0.041666667

Solving
0.2083333334 + x = 0.041666667

Solving for variable 'x'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + x = 0.041666667 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + x = 0.041666667 + -0.2083333334
x = 0.041666667 + -0.2083333334

Combine like terms: 0.041666667 + -0.2083333334 = -0.1666666664
x = -0.1666666664

Simplifying
x = -0.1666666664


Subproblem 2
x + 0.2083333334 = -0.041666667

Simplifying
x + 0.2083333334 = -0.041666667

Reorder the terms:
0.2083333334 + x = -0.041666667

Solving
0.2083333334 + x = -0.041666667

Solving for variable 'x'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + x = -0.041666667 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + x = -0.041666667 + -0.2083333334
x = -0.041666667 + -0.2083333334

Combine like terms: -0.041666667 + -0.2083333334 = -0.2500000004
x = -0.2500000004

Simplifying
x = -0.2500000004


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1666666664, -0.2500000004}

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