2x(x-3)=55-(x^2-4)

Solution for 2x(x-3)=55-(x^2-4) equation:

Simplifying
2x(x + -3) = 55 + -1(x2 + -4)

Reorder the terms:
2x(-3 + x) = 55 + -1(x2 + -4)
(-3 * 2x + x * 2x) = 55 + -1(x2 + -4)
(-6x + 2x2) = 55 + -1(x2 + -4)

Reorder the terms:
-6x + 2x2 = 55 + -1(-4 + x2)
-6x + 2x2 = 55 + (-4 * -1 + x2 * -1)
-6x + 2x2 = 55 + (4 + -1x2)

Combine like terms: 55 + 4 = 59
-6x + 2x2 = 59 + -1x2

Solving
-6x + 2x2 = 59 + -1x2

Solving for variable 'x'.

Reorder the terms:
-59 + -6x + 2x2 + x2 = 59 + -1x2 + -59 + x2

Combine like terms: 2x2 + x2 = 3x2
-59 + -6x + 3x2 = 59 + -1x2 + -59 + x2

Reorder the terms:
-59 + -6x + 3x2 = 59 + -59 + -1x2 + x2

Combine like terms: 59 + -59 = 0
-59 + -6x + 3x2 = 0 + -1x2 + x2
-59 + -6x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-59 + -6x + 3x2 = 0

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

Divide each side by '3'.
-19.66666667 + -2x + x2 = 0

Move the constant term to the right:

Add '19.66666667' to each side of the equation.
-19.66666667 + -2x + 19.66666667 + x2 = 0 + 19.66666667

Reorder the terms:
-19.66666667 + 19.66666667 + -2x + x2 = 0 + 19.66666667

Combine like terms: -19.66666667 + 19.66666667 = 0.00000000
0.00000000 + -2x + x2 = 0 + 19.66666667
-2x + x2 = 0 + 19.66666667

Combine like terms: 0 + 19.66666667 = 19.66666667
-2x + x2 = 19.66666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 19.66666667 + 1

Reorder the terms:
1 + -2x + x2 = 19.66666667 + 1

Combine like terms: 19.66666667 + 1 = 20.66666667
1 + -2x + x2 = 20.66666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 20.66666667

Calculate the square root of the right side: 4.546060566

Break this problem into two subproblems by setting 
(x + -1) equal to 4.546060566 and -4.546060566.

Subproblem 1
x + -1 = 4.546060566

Simplifying
x + -1 = 4.546060566

Reorder the terms:
-1 + x = 4.546060566

Solving
-1 + x = 4.546060566

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 4.546060566 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.546060566 + 1
x = 4.546060566 + 1

Combine like terms: 4.546060566 + 1 = 5.546060566
x = 5.546060566

Simplifying
x = 5.546060566

Subproblem 2
x + -1 = -4.546060566

Simplifying
x + -1 = -4.546060566

Reorder the terms:
-1 + x = -4.546060566

Solving
-1 + x = -4.546060566

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -4.546060566 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.546060566 + 1
x = -4.546060566 + 1

Combine like terms: -4.546060566 + 1 = -3.546060566
x = -3.546060566

Simplifying
x = -3.546060566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.546060566, -3.546060566}