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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 43.3 + -30.6 = 12.7
12.7 + -5.5339x + 4.6571x + 0.3259x2 + -0.3214x2 = 30.6 + -4.6571x + 0.3214x2 + -30.6 + 4.6571x + -0.3214x2

Combine like terms: -5.5339x + 4.6571x = -0.8768x
12.7 + -0.8768x + 0.3259x2 + -0.3214x2 = 30.6 + -4.6571x + 0.3214x2 + -30.6 + 4.6571x + -0.3214x2

Combine like terms: 0.3259x2 + -0.3214x2 = 0.0045x2
12.7 + -0.8768x + 0.0045x2 = 30.6 + -4.6571x + 0.3214x2 + -30.6 + 4.6571x + -0.3214x2

Reorder the terms:
12.7 + -0.8768x + 0.0045x2 = 30.6 + -30.6 + -4.6571x + 4.6571x + 0.3214x2 + -0.3214x2

Combine like terms: 30.6 + -30.6 = 0.0
12.7 + -0.8768x + 0.0045x2 = 0.0 + -4.6571x + 4.6571x + 0.3214x2 + -0.3214x2
12.7 + -0.8768x + 0.0045x2 = -4.6571x + 4.6571x + 0.3214x2 + -0.3214x2

Combine like terms: -4.6571x + 4.6571x = 0.0000
12.7 + -0.8768x + 0.0045x2 = 0.0000 + 0.3214x2 + -0.3214x2
12.7 + -0.8768x + 0.0045x2 = 0.3214x2 + -0.3214x2

Combine like terms: 0.3214x2 + -0.3214x2 = 0.0000
12.7 + -0.8768x + 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'.
2822.222222 + -194.8444444x + x2 = 0

Move the constant term to the right:

Add '-2822.222222' to each side of the equation.
2822.222222 + -194.8444444x + -2822.222222 + x2 = 0 + -2822.222222

Reorder the terms:
2822.222222 + -2822.222222 + -194.8444444x + x2 = 0 + -2822.222222

Combine like terms: 2822.222222 + -2822.222222 = 0.000000
0.000000 + -194.8444444x + x2 = 0 + -2822.222222
-194.8444444x + x2 = 0 + -2822.222222

Combine like terms: 0 + -2822.222222 = -2822.222222
-194.8444444x + x2 = -2822.222222

The x term is -194.8444444x.  Take half its coefficient (-97.4222222).
Square it (9491.089378) and add it to both sides.

Add '9491.089378' to each side of the equation.
-194.8444444x + 9491.089378 + x2 = -2822.222222 + 9491.089378

Reorder the terms:
9491.089378 + -194.8444444x + x2 = -2822.222222 + 9491.089378

Combine like terms: -2822.222222 + 9491.089378 = 6668.867156
9491.089378 + -194.8444444x + x2 = 6668.867156

Factor a perfect square on the left side:
(x + -97.4222222)(x + -97.4222222) = 6668.867156

Calculate the square root of the right side: 81.663132171

Break this problem into two subproblems by setting 
(x + -97.4222222) equal to 81.663132171 and -81.663132171.


Subproblem 1
x + -97.4222222 = 81.663132171

Simplifying
x + -97.4222222 = 81.663132171

Reorder the terms:
-97.4222222 + x = 81.663132171

Solving
-97.4222222 + x = 81.663132171

Solving for variable 'x'.

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

Add '97.4222222' to each side of the equation.
-97.4222222 + 97.4222222 + x = 81.663132171 + 97.4222222

Combine like terms: -97.4222222 + 97.4222222 = 0.0000000
0.0000000 + x = 81.663132171 + 97.4222222
x = 81.663132171 + 97.4222222

Combine like terms: 81.663132171 + 97.4222222 = 179.085354371
x = 179.085354371

Simplifying
x = 179.085354371


Subproblem 2
x + -97.4222222 = -81.663132171

Simplifying
x + -97.4222222 = -81.663132171

Reorder the terms:
-97.4222222 + x = -81.663132171

Solving
-97.4222222 + x = -81.663132171

Solving for variable 'x'.

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

Add '97.4222222' to each side of the equation.
-97.4222222 + 97.4222222 + x = -81.663132171 + 97.4222222

Combine like terms: -97.4222222 + 97.4222222 = 0.0000000
0.0000000 + x = -81.663132171 + 97.4222222
x = -81.663132171 + 97.4222222

Combine like terms: -81.663132171 + 97.4222222 = 15.759090029
x = 15.759090029

Simplifying
x = 15.759090029


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {179.085354371, 15.759090029}

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