81x^2+810x+1707=0

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Solution for 81x^2+810x+1707=0 equation: 


Simplifying
81x2 + 810x + 1707 = 0

Reorder the terms:
1707 + 810x + 81x2 = 0

Solving
1707 + 810x + 81x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(569 + 270x + 27x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(569 + 270x + 27x2)' equal to zero and attempt to solve:

Simplifying
569 + 270x + 27x2 = 0

Solving
569 + 270x + 27x2 = 0

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

Divide each side by '27'.
21.07407407 + 10x + x2 = 0

Move the constant term to the right:

Add '-21.07407407' to each side of the equation.
21.07407407 + 10x + -21.07407407 + x2 = 0 + -21.07407407

Reorder the terms:
21.07407407 + -21.07407407 + 10x + x2 = 0 + -21.07407407

Combine like terms: 21.07407407 + -21.07407407 = 0.00000000
0.00000000 + 10x + x2 = 0 + -21.07407407
10x + x2 = 0 + -21.07407407

Combine like terms: 0 + -21.07407407 = -21.07407407
10x + x2 = -21.07407407

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -21.07407407 + 25

Reorder the terms:
25 + 10x + x2 = -21.07407407 + 25

Combine like terms: -21.07407407 + 25 = 3.92592593
25 + 10x + x2 = 3.92592593

Factor a perfect square on the left side:
(x + 5)(x + 5) = 3.92592593

Calculate the square root of the right side: 1.981394945

Break this problem into two subproblems by setting 
(x + 5) equal to 1.981394945 and -1.981394945.


Subproblem 1
x + 5 = 1.981394945

Simplifying
x + 5 = 1.981394945

Reorder the terms:
5 + x = 1.981394945

Solving
5 + x = 1.981394945

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 1.981394945 + -5

Combine like terms: 5 + -5 = 0
0 + x = 1.981394945 + -5
x = 1.981394945 + -5

Combine like terms: 1.981394945 + -5 = -3.018605055
x = -3.018605055

Simplifying
x = -3.018605055


Subproblem 2
x + 5 = -1.981394945

Simplifying
x + 5 = -1.981394945

Reorder the terms:
5 + x = -1.981394945

Solving
5 + x = -1.981394945

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -1.981394945 + -5

Combine like terms: 5 + -5 = 0
0 + x = -1.981394945 + -5
x = -1.981394945 + -5

Combine like terms: -1.981394945 + -5 = -6.981394945
x = -6.981394945

Simplifying
x = -6.981394945


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.018605055, -6.981394945}
Solution
x = {-3.018605055, -6.981394945}

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