25x^2-30x-9=81

Solution for 25x^2-30x-9=81 equation:

Simplifying
25x2 + -30x + -9 = 81

Reorder the terms:
-9 + -30x + 25x2 = 81

Solving
-9 + -30x + 25x2 = 81

Solving for variable 'x'.

Reorder the terms:
-9 + -81 + -30x + 25x2 = 81 + -81

Combine like terms: -9 + -81 = -90
-90 + -30x + 25x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-90 + -30x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + -6x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-18 + -6x + 5x2)' equal to zero and attempt to solve:

Simplifying
-18 + -6x + 5x2 = 0

Solving
-18 + -6x + 5x2 = 0

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

Divide each side by '5'.
-3.6 + -1.2x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + -1.2x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + -1.2x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + -1.2x + x2 = 0 + 3.6
-1.2x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
-1.2x + x2 = 3.6

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 3.6 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 3.6 + 0.36

Combine like terms: 3.6 + 0.36 = 3.96
0.36 + -1.2x + x2 = 3.96

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 3.96

Calculate the square root of the right side: 1.989974874

Break this problem into two subproblems by setting 
(x + -0.6) equal to 1.989974874 and -1.989974874.

Subproblem 1
x + -0.6 = 1.989974874

Simplifying
x + -0.6 = 1.989974874

Reorder the terms:
-0.6 + x = 1.989974874

Solving
-0.6 + x = 1.989974874

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = 1.989974874 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = 1.989974874 + 0.6
x = 1.989974874 + 0.6

Combine like terms: 1.989974874 + 0.6 = 2.589974874
x = 2.589974874

Simplifying
x = 2.589974874

Subproblem 2
x + -0.6 = -1.989974874

Simplifying
x + -0.6 = -1.989974874

Reorder the terms:
-0.6 + x = -1.989974874

Solving
-0.6 + x = -1.989974874

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = -1.989974874 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = -1.989974874 + 0.6
x = -1.989974874 + 0.6

Combine like terms: -1.989974874 + 0.6 = -1.389974874
x = -1.389974874

Simplifying
x = -1.389974874

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.589974874, -1.389974874}
Solution
x = {2.589974874, -1.389974874}