81x^2+270x+175=0

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Solution for 81x^2+270x+175=0 equation: 


Simplifying
81x2 + 270x + 175 = 0

Reorder the terms:
175 + 270x + 81x2 = 0

Solving
175 + 270x + 81x2 = 0

Solving for variable 'x'.

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

Divide each side by '81'.
2.160493827 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.160493827' to each side of the equation.
2.160493827 + 3.333333333x + -2.160493827 + x2 = 0 + -2.160493827

Reorder the terms:
2.160493827 + -2.160493827 + 3.333333333x + x2 = 0 + -2.160493827

Combine like terms: 2.160493827 + -2.160493827 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + -2.160493827
3.333333333x + x2 = 0 + -2.160493827

Combine like terms: 0 + -2.160493827 = -2.160493827
3.333333333x + x2 = -2.160493827

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -2.160493827 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -2.160493827 + 2.777777779

Combine like terms: -2.160493827 + 2.777777779 = 0.617283952
2.777777779 + 3.333333333x + x2 = 0.617283952

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 0.617283952

Calculate the square root of the right side: 0.785674202

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 0.785674202 and -0.785674202.


Subproblem 1
x + 1.666666667 = 0.785674202

Simplifying
x + 1.666666667 = 0.785674202

Reorder the terms:
1.666666667 + x = 0.785674202

Solving
1.666666667 + x = 0.785674202

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 0.785674202 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 0.785674202 + -1.666666667
x = 0.785674202 + -1.666666667

Combine like terms: 0.785674202 + -1.666666667 = -0.880992465
x = -0.880992465

Simplifying
x = -0.880992465


Subproblem 2
x + 1.666666667 = -0.785674202

Simplifying
x + 1.666666667 = -0.785674202

Reorder the terms:
1.666666667 + x = -0.785674202

Solving
1.666666667 + x = -0.785674202

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -0.785674202 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -0.785674202 + -1.666666667
x = -0.785674202 + -1.666666667

Combine like terms: -0.785674202 + -1.666666667 = -2.452340869
x = -2.452340869

Simplifying
x = -2.452340869


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.880992465, -2.452340869}

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