.3214x^2-4.6571x+30.6=.3259x^2-5.5339+43.3

Solution for .3214x^2-4.6571x+30.6=.3259x^2-5.5339+43.3 equation:

Simplifying
0.3214x2 + -4.6571x + 30.6 = 0.3259x2 + -5.5339 + 43.3

Reorder the terms:
30.6 + -4.6571x + 0.3214x2 = 0.3259x2 + -5.5339 + 43.3

Reorder the terms:
30.6 + -4.6571x + 0.3214x2 = -5.5339 + 43.3 + 0.3259x2

Combine like terms: -5.5339 + 43.3 = 37.7661
30.6 + -4.6571x + 0.3214x2 = 37.7661 + 0.3259x2

Solving
30.6 + -4.6571x + 0.3214x2 = 37.7661 + 0.3259x2

Solving for variable 'x'.

Reorder the terms:
30.6 + -37.7661 + -4.6571x + 0.3214x2 + -0.3259x2 = 37.7661 + 0.3259x2 + -37.7661 + -0.3259x2

Combine like terms: 30.6 + -37.7661 = -7.1661
-7.1661 + -4.6571x + 0.3214x2 + -0.3259x2 = 37.7661 + 0.3259x2 + -37.7661 + -0.3259x2

Combine like terms: 0.3214x2 + -0.3259x2 = -0.0045x2
-7.1661 + -4.6571x + -0.0045x2 = 37.7661 + 0.3259x2 + -37.7661 + -0.3259x2

Reorder the terms:
-7.1661 + -4.6571x + -0.0045x2 = 37.7661 + -37.7661 + 0.3259x2 + -0.3259x2

Combine like terms: 37.7661 + -37.7661 = 0.0000
-7.1661 + -4.6571x + -0.0045x2 = 0.0000 + 0.3259x2 + -0.3259x2
-7.1661 + -4.6571x + -0.0045x2 = 0.3259x2 + -0.3259x2

Combine like terms: 0.3259x2 + -0.3259x2 = 0.0000
-7.1661 + -4.6571x + -0.0045x2 = 0.0000

Begin completing the square.  Divide all terms by
-0.0045 the coefficient of the squared term: 

Divide each side by '-0.0045'.
1592.466667 + 1034.911111x + x2 = 0

Move the constant term to the right:

Add '-1592.466667' to each side of the equation.
1592.466667 + 1034.911111x + -1592.466667 + x2 = 0 + -1592.466667

Reorder the terms:
1592.466667 + -1592.466667 + 1034.911111x + x2 = 0 + -1592.466667

Combine like terms: 1592.466667 + -1592.466667 = 0.000000
0.000000 + 1034.911111x + x2 = 0 + -1592.466667
1034.911111x + x2 = 0 + -1592.466667

Combine like terms: 0 + -1592.466667 = -1592.466667
1034.911111x + x2 = -1592.466667

The x term is 1034.911111x.  Take half its coefficient (517.4555555).
Square it (267760.2519) and add it to both sides.

Add '267760.2519' to each side of the equation.
1034.911111x + 267760.2519 + x2 = -1592.466667 + 267760.2519

Reorder the terms:
267760.2519 + 1034.911111x + x2 = -1592.466667 + 267760.2519

Combine like terms: -1592.466667 + 267760.2519 = 266167.785233
267760.2519 + 1034.911111x + x2 = 266167.785233

Factor a perfect square on the left side:
(x + 517.4555555)(x + 517.4555555) = 266167.785233

Calculate the square root of the right side: 515.914513493

Break this problem into two subproblems by setting 
(x + 517.4555555) equal to 515.914513493 and -515.914513493.

Subproblem 1
x + 517.4555555 = 515.914513493

Simplifying
x + 517.4555555 = 515.914513493

Reorder the terms:
517.4555555 + x = 515.914513493

Solving
517.4555555 + x = 515.914513493

Solving for variable 'x'.

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

Add '-517.4555555' to each side of the equation.
517.4555555 + -517.4555555 + x = 515.914513493 + -517.4555555

Combine like terms: 517.4555555 + -517.4555555 = 0.0000000
0.0000000 + x = 515.914513493 + -517.4555555
x = 515.914513493 + -517.4555555

Combine like terms: 515.914513493 + -517.4555555 = -1.541042007
x = -1.541042007

Simplifying
x = -1.541042007

Subproblem 2
x + 517.4555555 = -515.914513493

Simplifying
x + 517.4555555 = -515.914513493

Reorder the terms:
517.4555555 + x = -515.914513493

Solving
517.4555555 + x = -515.914513493

Solving for variable 'x'.

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

Add '-517.4555555' to each side of the equation.
517.4555555 + -517.4555555 + x = -515.914513493 + -517.4555555

Combine like terms: 517.4555555 + -517.4555555 = 0.0000000
0.0000000 + x = -515.914513493 + -517.4555555
x = -515.914513493 + -517.4555555

Combine like terms: -515.914513493 + -517.4555555 = -1033.370068993
x = -1033.370068993

Simplifying
x = -1033.370068993

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.541042007, -1033.370068993}