(2x-6)x-(x^2+2)=0

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Solution for (2x-6)x-(x^2+2)=0 equation:


Simplifying
(2x + -6) * x + -1(x2 + 2) = 0

Reorder the terms:
(-6 + 2x) * x + -1(x2 + 2) = 0

Reorder the terms for easier multiplication:
x(-6 + 2x) + -1(x2 + 2) = 0
(-6 * x + 2x * x) + -1(x2 + 2) = 0
(-6x + 2x2) + -1(x2 + 2) = 0

Reorder the terms:
-6x + 2x2 + -1(2 + x2) = 0
-6x + 2x2 + (2 * -1 + x2 * -1) = 0
-6x + 2x2 + (-2 + -1x2) = 0

Reorder the terms:
-2 + -6x + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
-2 + -6x + 1x2 = 0

Solving
-2 + -6x + 1x2 = 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 + -6x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -6x + x2 = 0 + 2

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

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

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 2 + 9

Reorder the terms:
9 + -6x + x2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + -6x + x2 = 11

Factor a perfect square on the left side:
(x + -3)(x + -3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -3) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + -3 = 3.31662479

Simplifying
x + -3 = 3.31662479

Reorder the terms:
-3 + x = 3.31662479

Solving
-3 + x = 3.31662479

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.31662479 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.31662479 + 3
x = 3.31662479 + 3

Combine like terms: 3.31662479 + 3 = 6.31662479
x = 6.31662479

Simplifying
x = 6.31662479


Subproblem 2
x + -3 = -3.31662479

Simplifying
x + -3 = -3.31662479

Reorder the terms:
-3 + x = -3.31662479

Solving
-3 + x = -3.31662479

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.31662479 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.31662479 + 3
x = -3.31662479 + 3

Combine like terms: -3.31662479 + 3 = -0.31662479
x = -0.31662479

Simplifying
x = -0.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.31662479, -0.31662479}

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