2=-0.25(X-4)(X-4)+4

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Solution for 2=-0.25(X-4)(X-4)+4 equation: 


Simplifying
2 = -0.25(X + -4)(X + -4) + 4

Reorder the terms:
2 = -0.25(-4 + X)(X + -4) + 4

Reorder the terms:
2 = -0.25(-4 + X)(-4 + X) + 4

Multiply (-4 + X) * (-4 + X)
2 = -0.25(-4(-4 + X) + X(-4 + X)) + 4
2 = -0.25((-4 * -4 + X * -4) + X(-4 + X)) + 4
2 = -0.25((16 + -4X) + X(-4 + X)) + 4
2 = -0.25(16 + -4X + (-4 * X + X * X)) + 4
2 = -0.25(16 + -4X + (-4X + X2)) + 4

Combine like terms: -4X + -4X = -8X
2 = -0.25(16 + -8X + X2) + 4
2 = (16 * -0.25 + -8X * -0.25 + X2 * -0.25) + 4
2 = (-4 + 2X + -0.25X2) + 4

Reorder the terms:
2 = -4 + 4 + 2X + -0.25X2

Combine like terms: -4 + 4 = 0
2 = 0 + 2X + -0.25X2
2 = 2X + -0.25X2

Solving
2 = 2X + -0.25X2

Solving for variable 'X'.

Reorder the terms:
2 + -2X + 0.25X2 = 2X + -2X + -0.25X2 + 0.25X2

Combine like terms: 2X + -2X = 0
2 + -2X + 0.25X2 = 0 + -0.25X2 + 0.25X2
2 + -2X + 0.25X2 = -0.25X2 + 0.25X2

Combine like terms: -0.25X2 + 0.25X2 = 0.00
2 + -2X + 0.25X2 = 0.00

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

Divide each side by '0.25'.
8 + -8X + X2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -8X + -8 + X2 = 0 + -8

Reorder the terms:
8 + -8 + -8X + X2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -8X + X2 = 0 + -8
-8X + X2 = 0 + -8

Combine like terms: 0 + -8 = -8
-8X + X2 = -8

The X term is -8X.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8X + 16 + X2 = -8 + 16

Reorder the terms:
16 + -8X + X2 = -8 + 16

Combine like terms: -8 + 16 = 8
16 + -8X + X2 = 8

Factor a perfect square on the left side:
(X + -4)(X + -4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(X + -4) equal to 2.828427125 and -2.828427125.


Subproblem 1
X + -4 = 2.828427125

Simplifying
X + -4 = 2.828427125

Reorder the terms:
-4 + X = 2.828427125

Solving
-4 + X = 2.828427125

Solving for variable 'X'.

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

Add '4' to each side of the equation.
-4 + 4 + X = 2.828427125 + 4

Combine like terms: -4 + 4 = 0
0 + X = 2.828427125 + 4
X = 2.828427125 + 4

Combine like terms: 2.828427125 + 4 = 6.828427125
X = 6.828427125

Simplifying
X = 6.828427125


Subproblem 2
X + -4 = -2.828427125

Simplifying
X + -4 = -2.828427125

Reorder the terms:
-4 + X = -2.828427125

Solving
-4 + X = -2.828427125

Solving for variable 'X'.

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

Add '4' to each side of the equation.
-4 + 4 + X = -2.828427125 + 4

Combine like terms: -4 + 4 = 0
0 + X = -2.828427125 + 4
X = -2.828427125 + 4

Combine like terms: -2.828427125 + 4 = 1.171572875
X = 1.171572875

Simplifying
X = 1.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {6.828427125, 1.171572875}

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