0.0079x^2+0.057x=629.5-0.054x^2

Solution for 0.0079x^2+0.057x=629.5-0.054x^2 equation:

Simplifying
0.0079x2 + 0.057x = 629.5 + -0.054x2

Reorder the terms:
0.057x + 0.0079x2 = 629.5 + -0.054x2

Solving
0.057x + 0.0079x2 = 629.5 + -0.054x2

Solving for variable 'x'.

Reorder the terms:
-629.5 + 0.057x + 0.0079x2 + 0.054x2 = 629.5 + -0.054x2 + -629.5 + 0.054x2

Combine like terms: 0.0079x2 + 0.054x2 = 0.0619x2
-629.5 + 0.057x + 0.0619x2 = 629.5 + -0.054x2 + -629.5 + 0.054x2

Reorder the terms:
-629.5 + 0.057x + 0.0619x2 = 629.5 + -629.5 + -0.054x2 + 0.054x2

Combine like terms: 629.5 + -629.5 = 0.0
-629.5 + 0.057x + 0.0619x2 = 0.0 + -0.054x2 + 0.054x2
-629.5 + 0.057x + 0.0619x2 = -0.054x2 + 0.054x2

Combine like terms: -0.054x2 + 0.054x2 = 0.000
-629.5 + 0.057x + 0.0619x2 = 0.000

Begin completing the square.  Divide all terms by
0.0619 the coefficient of the squared term: 

Divide each side by '0.0619'.
-10169.62843 + 0.9208400646x + x2 = 0

Move the constant term to the right:

Add '10169.62843' to each side of the equation.
-10169.62843 + 0.9208400646x + 10169.62843 + x2 = 0 + 10169.62843

Reorder the terms:
-10169.62843 + 10169.62843 + 0.9208400646x + x2 = 0 + 10169.62843

Combine like terms: -10169.62843 + 10169.62843 = 0.00000
0.00000 + 0.9208400646x + x2 = 0 + 10169.62843
0.9208400646x + x2 = 0 + 10169.62843

Combine like terms: 0 + 10169.62843 = 10169.62843
0.9208400646x + x2 = 10169.62843

The x term is 0.9208400646x.  Take half its coefficient (0.4604200323).
Square it (0.2119866061) and add it to both sides.

Add '0.2119866061' to each side of the equation.
0.9208400646x + 0.2119866061 + x2 = 10169.62843 + 0.2119866061

Reorder the terms:
0.2119866061 + 0.9208400646x + x2 = 10169.62843 + 0.2119866061

Combine like terms: 10169.62843 + 0.2119866061 = 10169.8404166061
0.2119866061 + 0.9208400646x + x2 = 10169.8404166061

Factor a perfect square on the left side:
(x + 0.4604200323)(x + 0.4604200323) = 10169.8404166061

Calculate the square root of the right side: 100.845626661

Break this problem into two subproblems by setting 
(x + 0.4604200323) equal to 100.845626661 and -100.845626661.

Subproblem 1
x + 0.4604200323 = 100.845626661

Simplifying
x + 0.4604200323 = 100.845626661

Reorder the terms:
0.4604200323 + x = 100.845626661

Solving
0.4604200323 + x = 100.845626661

Solving for variable 'x'.

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

Add '-0.4604200323' to each side of the equation.
0.4604200323 + -0.4604200323 + x = 100.845626661 + -0.4604200323

Combine like terms: 0.4604200323 + -0.4604200323 = 0.0000000000
0.0000000000 + x = 100.845626661 + -0.4604200323
x = 100.845626661 + -0.4604200323

Combine like terms: 100.845626661 + -0.4604200323 = 100.3852066287
x = 100.3852066287

Simplifying
x = 100.3852066287

Subproblem 2
x + 0.4604200323 = -100.845626661

Simplifying
x + 0.4604200323 = -100.845626661

Reorder the terms:
0.4604200323 + x = -100.845626661

Solving
0.4604200323 + x = -100.845626661

Solving for variable 'x'.

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

Add '-0.4604200323' to each side of the equation.
0.4604200323 + -0.4604200323 + x = -100.845626661 + -0.4604200323

Combine like terms: 0.4604200323 + -0.4604200323 = 0.0000000000
0.0000000000 + x = -100.845626661 + -0.4604200323
x = -100.845626661 + -0.4604200323

Combine like terms: -100.845626661 + -0.4604200323 = -101.3060466933
x = -101.3060466933

Simplifying
x = -101.3060466933

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {100.3852066287, -101.3060466933}