x^2-4=0.5x+2

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


Simplifying
x2 + -4 = 0.5x + 2

Reorder the terms:
-4 + x2 = 0.5x + 2

Reorder the terms:
-4 + x2 = 2 + 0.5x

Solving
-4 + x2 = 2 + 0.5x

Solving for variable 'x'.

Reorder the terms:
-4 + -2 + -0.5x + x2 = 2 + 0.5x + -2 + -0.5x

Combine like terms: -4 + -2 = -6
-6 + -0.5x + x2 = 2 + 0.5x + -2 + -0.5x

Reorder the terms:
-6 + -0.5x + x2 = 2 + -2 + 0.5x + -0.5x

Combine like terms: 2 + -2 = 0
-6 + -0.5x + x2 = 0 + 0.5x + -0.5x
-6 + -0.5x + x2 = 0.5x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
-6 + -0.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -0.5x + 6 + x2 = 0.0 + 6

Reorder the terms:
-6 + 6 + -0.5x + x2 = 0.0 + 6

Combine like terms: -6 + 6 = 0
0 + -0.5x + x2 = 0.0 + 6
-0.5x + x2 = 0.0 + 6

Combine like terms: 0.0 + 6 = 6
-0.5x + x2 = 6

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 = 6 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 6 + 0.0625

Combine like terms: 6 + 0.0625 = 6.0625
0.0625 + -0.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.46221445 and -2.46221445.


Subproblem 1
x + -0.25 = 2.46221445

Simplifying
x + -0.25 = 2.46221445

Reorder the terms:
-0.25 + x = 2.46221445

Solving
-0.25 + x = 2.46221445

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 = 2.46221445 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 2.46221445 + 0.25
x = 2.46221445 + 0.25

Combine like terms: 2.46221445 + 0.25 = 2.71221445
x = 2.71221445

Simplifying
x = 2.71221445


Subproblem 2
x + -0.25 = -2.46221445

Simplifying
x + -0.25 = -2.46221445

Reorder the terms:
-0.25 + x = -2.46221445

Solving
-0.25 + x = -2.46221445

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 = -2.46221445 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -2.46221445 + 0.25
x = -2.46221445 + 0.25

Combine like terms: -2.46221445 + 0.25 = -2.21221445
x = -2.21221445

Simplifying
x = -2.21221445


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.71221445, -2.21221445}

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