0=276x^2+2x-0.25

Solution for 0=276x^2+2x-0.25 equation:

Simplifying
0 = 276x2 + 2x + -0.25

Reorder the terms:
0 = -0.25 + 2x + 276x2

Solving
0 = -0.25 + 2x + 276x2

Solving for variable 'x'.

Combine like terms: 0 + 0.25 = 0.25
0.25 + -2x + -276x2 = -0.25 + 2x + 276x2 + 0.25 + -2x + -276x2

Reorder the terms:
0.25 + -2x + -276x2 = -0.25 + 0.25 + 2x + -2x + 276x2 + -276x2

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -2x + -276x2 = 0.00 + 2x + -2x + 276x2 + -276x2
0.25 + -2x + -276x2 = 2x + -2x + 276x2 + -276x2

Combine like terms: 2x + -2x = 0
0.25 + -2x + -276x2 = 0 + 276x2 + -276x2
0.25 + -2x + -276x2 = 276x2 + -276x2

Combine like terms: 276x2 + -276x2 = 0
0.25 + -2x + -276x2 = 0

Begin completing the square.  Divide all terms by
-276 the coefficient of the squared term: 

Divide each side by '-276'.
-0.0009057971014 + 0.007246376812x + x2 = 0

Move the constant term to the right:

Add '0.0009057971014' to each side of the equation.
-0.0009057971014 + 0.007246376812x + 0.0009057971014 + x2 = 0 + 0.0009057971014

Reorder the terms:
-0.0009057971014 + 0.0009057971014 + 0.007246376812x + x2 = 0 + 0.0009057971014

Combine like terms: -0.0009057971014 + 0.0009057971014 = 0.0000000000000
0.0000000000000 + 0.007246376812x + x2 = 0 + 0.0009057971014
0.007246376812x + x2 = 0 + 0.0009057971014

Combine like terms: 0 + 0.0009057971014 = 0.0009057971014
0.007246376812x + x2 = 0.0009057971014

The x term is 0.007246376812x.  Take half its coefficient (0.003623188406).
Square it (0.00001312749423) and add it to both sides.

Add '0.00001312749423' to each side of the equation.
0.007246376812x + 0.00001312749423 + x2 = 0.0009057971014 + 0.00001312749423

Reorder the terms:
0.00001312749423 + 0.007246376812x + x2 = 0.0009057971014 + 0.00001312749423

Combine like terms: 0.0009057971014 + 0.00001312749423 = 0.00091892459563
0.00001312749423 + 0.007246376812x + x2 = 0.00091892459563

Factor a perfect square on the left side:
(x + 0.003623188406)(x + 0.003623188406) = 0.00091892459563

Calculate the square root of the right side: 0.030313769

Break this problem into two subproblems by setting 
(x + 0.003623188406) equal to 0.030313769 and -0.030313769.

Subproblem 1
x + 0.003623188406 = 0.030313769

Simplifying
x + 0.003623188406 = 0.030313769

Reorder the terms:
0.003623188406 + x = 0.030313769

Solving
0.003623188406 + x = 0.030313769

Solving for variable 'x'.

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

Add '-0.003623188406' to each side of the equation.
0.003623188406 + -0.003623188406 + x = 0.030313769 + -0.003623188406

Combine like terms: 0.003623188406 + -0.003623188406 = 0.000000000000
0.000000000000 + x = 0.030313769 + -0.003623188406
x = 0.030313769 + -0.003623188406

Combine like terms: 0.030313769 + -0.003623188406 = 0.026690580594
x = 0.026690580594

Simplifying
x = 0.026690580594

Subproblem 2
x + 0.003623188406 = -0.030313769

Simplifying
x + 0.003623188406 = -0.030313769

Reorder the terms:
0.003623188406 + x = -0.030313769

Solving
0.003623188406 + x = -0.030313769

Solving for variable 'x'.

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

Add '-0.003623188406' to each side of the equation.
0.003623188406 + -0.003623188406 + x = -0.030313769 + -0.003623188406

Combine like terms: 0.003623188406 + -0.003623188406 = 0.000000000000
0.000000000000 + x = -0.030313769 + -0.003623188406
x = -0.030313769 + -0.003623188406

Combine like terms: -0.030313769 + -0.003623188406 = -0.033936957406
x = -0.033936957406

Simplifying
x = -0.033936957406

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.026690580594, -0.033936957406}