x^2+0.5x-4=0

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Solution for x^2+0.5x-4=0 equation: 


Simplifying
x2 + 0.5x + -4 = 0

Reorder the terms:
-4 + 0.5x + x2 = 0

Solving
-4 + 0.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.5x + x2 = 0 + 4
0.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.5x + x2 = 4

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 4 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 4 + 0.0625

Combine like terms: 4 + 0.0625 = 4.0625
0.0625 + 0.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.015564437 and -2.015564437.


Subproblem 1
x + 0.25 = 2.015564437

Simplifying
x + 0.25 = 2.015564437

Reorder the terms:
0.25 + x = 2.015564437

Solving
0.25 + x = 2.015564437

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 2.015564437 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 2.015564437 + -0.25
x = 2.015564437 + -0.25

Combine like terms: 2.015564437 + -0.25 = 1.765564437
x = 1.765564437

Simplifying
x = 1.765564437


Subproblem 2
x + 0.25 = -2.015564437

Simplifying
x + 0.25 = -2.015564437

Reorder the terms:
0.25 + x = -2.015564437

Solving
0.25 + x = -2.015564437

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -2.015564437 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -2.015564437 + -0.25
x = -2.015564437 + -0.25

Combine like terms: -2.015564437 + -0.25 = -2.265564437
x = -2.265564437

Simplifying
x = -2.265564437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.765564437, -2.265564437}

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