288661.199=732.216x^2+2687.049x+3056.333

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Solution for 288661.199=732.216x^2+2687.049x+3056.333 equation: 


Simplifying
288661.199 = 732.216x2 + 2687.049x + 3056.333

Reorder the terms:
288661.199 = 3056.333 + 2687.049x + 732.216x2

Solving
288661.199 = 3056.333 + 2687.049x + 732.216x2

Solving for variable 'x'.

Combine like terms: 288661.199 + -3056.333 = 285604.866
285604.866 + -2687.049x + -732.216x2 = 3056.333 + 2687.049x + 732.216x2 + -3056.333 + -2687.049x + -732.216x2

Reorder the terms:
285604.866 + -2687.049x + -732.216x2 = 3056.333 + -3056.333 + 2687.049x + -2687.049x + 732.216x2 + -732.216x2

Combine like terms: 3056.333 + -3056.333 = 0.000
285604.866 + -2687.049x + -732.216x2 = 0.000 + 2687.049x + -2687.049x + 732.216x2 + -732.216x2
285604.866 + -2687.049x + -732.216x2 = 2687.049x + -2687.049x + 732.216x2 + -732.216x2

Combine like terms: 2687.049x + -2687.049x = 0.000
285604.866 + -2687.049x + -732.216x2 = 0.000 + 732.216x2 + -732.216x2
285604.866 + -2687.049x + -732.216x2 = 732.216x2 + -732.216x2

Combine like terms: 732.216x2 + -732.216x2 = 0.000
285604.866 + -2687.049x + -732.216x2 = 0.000

Begin completing the square.  Divide all terms by
-732.216 the coefficient of the squared term: 

Divide each side by '-732.216'.
-390.0554836 + 3.66974909x + x2 = 0

Move the constant term to the right:

Add '390.0554836' to each side of the equation.
-390.0554836 + 3.66974909x + 390.0554836 + x2 = 0 + 390.0554836

Reorder the terms:
-390.0554836 + 390.0554836 + 3.66974909x + x2 = 0 + 390.0554836

Combine like terms: -390.0554836 + 390.0554836 = 0.0000000
0.0000000 + 3.66974909x + x2 = 0 + 390.0554836
3.66974909x + x2 = 0 + 390.0554836

Combine like terms: 0 + 390.0554836 = 390.0554836
3.66974909x + x2 = 390.0554836

The x term is 3.66974909x.  Take half its coefficient (1.834874545).
Square it (3.366764596) and add it to both sides.

Add '3.366764596' to each side of the equation.
3.66974909x + 3.366764596 + x2 = 390.0554836 + 3.366764596

Reorder the terms:
3.366764596 + 3.66974909x + x2 = 390.0554836 + 3.366764596

Combine like terms: 390.0554836 + 3.366764596 = 393.422248196
3.366764596 + 3.66974909x + x2 = 393.422248196

Factor a perfect square on the left side:
(x + 1.834874545)(x + 1.834874545) = 393.422248196

Calculate the square root of the right side: 19.834874544

Break this problem into two subproblems by setting 
(x + 1.834874545) equal to 19.834874544 and -19.834874544.


Subproblem 1
x + 1.834874545 = 19.834874544

Simplifying
x + 1.834874545 = 19.834874544

Reorder the terms:
1.834874545 + x = 19.834874544

Solving
1.834874545 + x = 19.834874544

Solving for variable 'x'.

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

Add '-1.834874545' to each side of the equation.
1.834874545 + -1.834874545 + x = 19.834874544 + -1.834874545

Combine like terms: 1.834874545 + -1.834874545 = 0.000000000
0.000000000 + x = 19.834874544 + -1.834874545
x = 19.834874544 + -1.834874545

Combine like terms: 19.834874544 + -1.834874545 = 17.999999999
x = 17.999999999

Simplifying
x = 17.999999999


Subproblem 2
x + 1.834874545 = -19.834874544

Simplifying
x + 1.834874545 = -19.834874544

Reorder the terms:
1.834874545 + x = -19.834874544

Solving
1.834874545 + x = -19.834874544

Solving for variable 'x'.

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

Add '-1.834874545' to each side of the equation.
1.834874545 + -1.834874545 + x = -19.834874544 + -1.834874545

Combine like terms: 1.834874545 + -1.834874545 = 0.000000000
0.000000000 + x = -19.834874544 + -1.834874545
x = -19.834874544 + -1.834874545

Combine like terms: -19.834874544 + -1.834874545 = -21.669749089
x = -21.669749089

Simplifying
x = -21.669749089


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.999999999, -21.669749089}

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