5.600+170x-3x^2=0

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Solution for 5.600+170x-3x^2=0 equation: 


Simplifying
5.600 + 170x + -3x2 = 0

Solving
5.600 + 170x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1.866666667 + -56.66666667x + x2 = 0

Move the constant term to the right:

Add '1.866666667' to each side of the equation.
-1.866666667 + -56.66666667x + 1.866666667 + x2 = 0 + 1.866666667

Reorder the terms:
-1.866666667 + 1.866666667 + -56.66666667x + x2 = 0 + 1.866666667

Combine like terms: -1.866666667 + 1.866666667 = 0.000000000
0.000000000 + -56.66666667x + x2 = 0 + 1.866666667
-56.66666667x + x2 = 0 + 1.866666667

Combine like terms: 0 + 1.866666667 = 1.866666667
-56.66666667x + x2 = 1.866666667

The x term is -56.66666667x.  Take half its coefficient (-28.33333334).
Square it (802.7777782) and add it to both sides.

Add '802.7777782' to each side of the equation.
-56.66666667x + 802.7777782 + x2 = 1.866666667 + 802.7777782

Reorder the terms:
802.7777782 + -56.66666667x + x2 = 1.866666667 + 802.7777782

Combine like terms: 1.866666667 + 802.7777782 = 804.644444867
802.7777782 + -56.66666667x + x2 = 804.644444867

Factor a perfect square on the left side:
(x + -28.33333334)(x + -28.33333334) = 804.644444867

Calculate the square root of the right side: 28.36625539

Break this problem into two subproblems by setting 
(x + -28.33333334) equal to 28.36625539 and -28.36625539.


Subproblem 1
x + -28.33333334 = 28.36625539

Simplifying
x + -28.33333334 = 28.36625539

Reorder the terms:
-28.33333334 + x = 28.36625539

Solving
-28.33333334 + x = 28.36625539

Solving for variable 'x'.

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

Add '28.33333334' to each side of the equation.
-28.33333334 + 28.33333334 + x = 28.36625539 + 28.33333334

Combine like terms: -28.33333334 + 28.33333334 = 0.00000000
0.00000000 + x = 28.36625539 + 28.33333334
x = 28.36625539 + 28.33333334

Combine like terms: 28.36625539 + 28.33333334 = 56.69958873
x = 56.69958873

Simplifying
x = 56.69958873


Subproblem 2
x + -28.33333334 = -28.36625539

Simplifying
x + -28.33333334 = -28.36625539

Reorder the terms:
-28.33333334 + x = -28.36625539

Solving
-28.33333334 + x = -28.36625539

Solving for variable 'x'.

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

Add '28.33333334' to each side of the equation.
-28.33333334 + 28.33333334 + x = -28.36625539 + 28.33333334

Combine like terms: -28.33333334 + 28.33333334 = 0.00000000
0.00000000 + x = -28.36625539 + 28.33333334
x = -28.36625539 + 28.33333334

Combine like terms: -28.36625539 + 28.33333334 = -0.03292205
x = -0.03292205

Simplifying
x = -0.03292205


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.69958873, -0.03292205}

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