x^2+0.25x-3=0

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Solution for x^2+0.25x-3=0 equation: 


Simplifying
x2 + 0.25x + -3 = 0

Reorder the terms:
-3 + 0.25x + x2 = 0

Solving
-3 + 0.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 0.25x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 0.25x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 0.25x + x2 = 0 + 3
0.25x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
0.25x + x2 = 3

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 3 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 3 + 0.015625

Combine like terms: 3 + 0.015625 = 3.015625
0.015625 + 0.25x + x2 = 3.015625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 3.015625

Calculate the square root of the right side: 1.736555499

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.736555499 and -1.736555499.


Subproblem 1
x + 0.125 = 1.736555499

Simplifying
x + 0.125 = 1.736555499

Reorder the terms:
0.125 + x = 1.736555499

Solving
0.125 + x = 1.736555499

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 1.736555499 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 1.736555499 + -0.125
x = 1.736555499 + -0.125

Combine like terms: 1.736555499 + -0.125 = 1.611555499
x = 1.611555499

Simplifying
x = 1.611555499


Subproblem 2
x + 0.125 = -1.736555499

Simplifying
x + 0.125 = -1.736555499

Reorder the terms:
0.125 + x = -1.736555499

Solving
0.125 + x = -1.736555499

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -1.736555499 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -1.736555499 + -0.125
x = -1.736555499 + -0.125

Combine like terms: -1.736555499 + -0.125 = -1.861555499
x = -1.861555499

Simplifying
x = -1.861555499


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.611555499, -1.861555499}

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