x^2=19.188-63.96x+53.3x^2

Solution for x^2=19.188-63.96x+53.3x^2 equation:

Simplifying
x2 = 19.188 + -63.96x + 53.3x2

Solving
x2 = 19.188 + -63.96x + 53.3x2

Solving for variable 'x'.

Reorder the terms:
-19.188 + 63.96x + x2 + -53.3x2 = 19.188 + -63.96x + 53.3x2 + -19.188 + 63.96x + -53.3x2

Combine like terms: x2 + -53.3x2 = -52.3x2
-19.188 + 63.96x + -52.3x2 = 19.188 + -63.96x + 53.3x2 + -19.188 + 63.96x + -53.3x2

Reorder the terms:
-19.188 + 63.96x + -52.3x2 = 19.188 + -19.188 + -63.96x + 63.96x + 53.3x2 + -53.3x2

Combine like terms: 19.188 + -19.188 = 0.000
-19.188 + 63.96x + -52.3x2 = 0.000 + -63.96x + 63.96x + 53.3x2 + -53.3x2
-19.188 + 63.96x + -52.3x2 = -63.96x + 63.96x + 53.3x2 + -53.3x2

Combine like terms: -63.96x + 63.96x = 0.00
-19.188 + 63.96x + -52.3x2 = 0.00 + 53.3x2 + -53.3x2
-19.188 + 63.96x + -52.3x2 = 53.3x2 + -53.3x2

Combine like terms: 53.3x2 + -53.3x2 = 0.0
-19.188 + 63.96x + -52.3x2 = 0.0

Begin completing the square.  Divide all terms by
-52.3 the coefficient of the squared term: 

Divide each side by '-52.3'.
0.3668833652 + -1.222944551x + x2 = 0

Move the constant term to the right:

Add '-0.3668833652' to each side of the equation.
0.3668833652 + -1.222944551x + -0.3668833652 + x2 = 0 + -0.3668833652

Reorder the terms:
0.3668833652 + -0.3668833652 + -1.222944551x + x2 = 0 + -0.3668833652

Combine like terms: 0.3668833652 + -0.3668833652 = 0.0000000000
0.0000000000 + -1.222944551x + x2 = 0 + -0.3668833652
-1.222944551x + x2 = 0 + -0.3668833652

Combine like terms: 0 + -0.3668833652 = -0.3668833652
-1.222944551x + x2 = -0.3668833652

The x term is -1.222944551x.  Take half its coefficient (-0.6114722755).
Square it (0.3738983437) and add it to both sides.

Add '0.3738983437' to each side of the equation.
-1.222944551x + 0.3738983437 + x2 = -0.3668833652 + 0.3738983437

Reorder the terms:
0.3738983437 + -1.222944551x + x2 = -0.3668833652 + 0.3738983437

Combine like terms: -0.3668833652 + 0.3738983437 = 0.0070149785
0.3738983437 + -1.222944551x + x2 = 0.0070149785

Factor a perfect square on the left side:
(x + -0.6114722755)(x + -0.6114722755) = 0.0070149785

Calculate the square root of the right side: 0.083755468

Break this problem into two subproblems by setting 
(x + -0.6114722755) equal to 0.083755468 and -0.083755468.

Subproblem 1
x + -0.6114722755 = 0.083755468

Simplifying
x + -0.6114722755 = 0.083755468

Reorder the terms:
-0.6114722755 + x = 0.083755468

Solving
-0.6114722755 + x = 0.083755468

Solving for variable 'x'.

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

Add '0.6114722755' to each side of the equation.
-0.6114722755 + 0.6114722755 + x = 0.083755468 + 0.6114722755

Combine like terms: -0.6114722755 + 0.6114722755 = 0.0000000000
0.0000000000 + x = 0.083755468 + 0.6114722755
x = 0.083755468 + 0.6114722755

Combine like terms: 0.083755468 + 0.6114722755 = 0.6952277435
x = 0.6952277435

Simplifying
x = 0.6952277435

Subproblem 2
x + -0.6114722755 = -0.083755468

Simplifying
x + -0.6114722755 = -0.083755468

Reorder the terms:
-0.6114722755 + x = -0.083755468

Solving
-0.6114722755 + x = -0.083755468

Solving for variable 'x'.

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

Add '0.6114722755' to each side of the equation.
-0.6114722755 + 0.6114722755 + x = -0.083755468 + 0.6114722755

Combine like terms: -0.6114722755 + 0.6114722755 = 0.0000000000
0.0000000000 + x = -0.083755468 + 0.6114722755
x = -0.083755468 + 0.6114722755

Combine like terms: -0.083755468 + 0.6114722755 = 0.5277168075
x = 0.5277168075

Simplifying
x = 0.5277168075

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6952277435, 0.5277168075}