x^2+0.25x-2=0

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


Simplifying
x2 + 0.25x + -2 = 0

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

Solving
-2 + 0.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.25x + 2 + x2 = 0 + 2

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

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

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

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 = 2 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 2 + 0.015625

Combine like terms: 2 + 0.015625 = 2.015625
0.015625 + 0.25x + x2 = 2.015625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.419727086 and -1.419727086.


Subproblem 1
x + 0.125 = 1.419727086

Simplifying
x + 0.125 = 1.419727086

Reorder the terms:
0.125 + x = 1.419727086

Solving
0.125 + x = 1.419727086

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 = 1.419727086 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 1.419727086 + -0.125
x = 1.419727086 + -0.125

Combine like terms: 1.419727086 + -0.125 = 1.294727086
x = 1.294727086

Simplifying
x = 1.294727086


Subproblem 2
x + 0.125 = -1.419727086

Simplifying
x + 0.125 = -1.419727086

Reorder the terms:
0.125 + x = -1.419727086

Solving
0.125 + x = -1.419727086

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 = -1.419727086 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -1.419727086 + -0.125
x = -1.419727086 + -0.125

Combine like terms: -1.419727086 + -0.125 = -1.544727086
x = -1.544727086

Simplifying
x = -1.544727086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.294727086, -1.544727086}

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