.56x^2-3.2x+708.28=707

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Solution for .56x^2-3.2x+708.28=707 equation: 


Simplifying
0.56x2 + -3.2x + 708.28 = 707

Reorder the terms:
708.28 + -3.2x + 0.56x2 = 707

Solving
708.28 + -3.2x + 0.56x2 = 707

Solving for variable 'x'.

Reorder the terms:
708.28 + -707 + -3.2x + 0.56x2 = 707 + -707

Combine like terms: 708.28 + -707 = 1.28
1.28 + -3.2x + 0.56x2 = 707 + -707

Combine like terms: 707 + -707 = 0
1.28 + -3.2x + 0.56x2 = 0

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

Divide each side by '0.56'.
2.285714286 + -5.714285714x + x2 = 0

Move the constant term to the right:

Add '-2.285714286' to each side of the equation.
2.285714286 + -5.714285714x + -2.285714286 + x2 = 0 + -2.285714286

Reorder the terms:
2.285714286 + -2.285714286 + -5.714285714x + x2 = 0 + -2.285714286

Combine like terms: 2.285714286 + -2.285714286 = 0.000000000
0.000000000 + -5.714285714x + x2 = 0 + -2.285714286
-5.714285714x + x2 = 0 + -2.285714286

Combine like terms: 0 + -2.285714286 = -2.285714286
-5.714285714x + x2 = -2.285714286

The x term is -5.714285714x.  Take half its coefficient (-2.857142857).
Square it (8.163265305) and add it to both sides.

Add '8.163265305' to each side of the equation.
-5.714285714x + 8.163265305 + x2 = -2.285714286 + 8.163265305

Reorder the terms:
8.163265305 + -5.714285714x + x2 = -2.285714286 + 8.163265305

Combine like terms: -2.285714286 + 8.163265305 = 5.877551019
8.163265305 + -5.714285714x + x2 = 5.877551019

Factor a perfect square on the left side:
(x + -2.857142857)(x + -2.857142857) = 5.877551019

Calculate the square root of the right side: 2.424366107

Break this problem into two subproblems by setting 
(x + -2.857142857) equal to 2.424366107 and -2.424366107.


Subproblem 1
x + -2.857142857 = 2.424366107

Simplifying
x + -2.857142857 = 2.424366107

Reorder the terms:
-2.857142857 + x = 2.424366107

Solving
-2.857142857 + x = 2.424366107

Solving for variable 'x'.

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

Add '2.857142857' to each side of the equation.
-2.857142857 + 2.857142857 + x = 2.424366107 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + x = 2.424366107 + 2.857142857
x = 2.424366107 + 2.857142857

Combine like terms: 2.424366107 + 2.857142857 = 5.281508964
x = 5.281508964

Simplifying
x = 5.281508964


Subproblem 2
x + -2.857142857 = -2.424366107

Simplifying
x + -2.857142857 = -2.424366107

Reorder the terms:
-2.857142857 + x = -2.424366107

Solving
-2.857142857 + x = -2.424366107

Solving for variable 'x'.

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

Add '2.857142857' to each side of the equation.
-2.857142857 + 2.857142857 + x = -2.424366107 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + x = -2.424366107 + 2.857142857
x = -2.424366107 + 2.857142857

Combine like terms: -2.424366107 + 2.857142857 = 0.43277675
x = 0.43277675

Simplifying
x = 0.43277675


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.281508964, 0.43277675}

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