25x^2+110x-90=0

Solution for 25x^2+110x-90=0 equation:

Simplifying
25x2 + 110x + -90 = 0

Reorder the terms:
-90 + 110x + 25x2 = 0

Solving
-90 + 110x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + 22x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-18 + 22x + 5x2)' equal to zero and attempt to solve:

Simplifying
-18 + 22x + 5x2 = 0

Solving
-18 + 22x + 5x2 = 0

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

Divide each side by '5'.
-3.6 + 4.4x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 4.4x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 4.4x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 4.4x + x2 = 0 + 3.6
4.4x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
4.4x + x2 = 3.6

The x term is 4.4x.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4x + 4.84 + x2 = 3.6 + 4.84

Reorder the terms:
4.84 + 4.4x + x2 = 3.6 + 4.84

Combine like terms: 3.6 + 4.84 = 8.44
4.84 + 4.4x + x2 = 8.44

Factor a perfect square on the left side:
(x + 2.2)(x + 2.2) = 8.44

Calculate the square root of the right side: 2.905167809

Break this problem into two subproblems by setting 
(x + 2.2) equal to 2.905167809 and -2.905167809.

Subproblem 1
x + 2.2 = 2.905167809

Simplifying
x + 2.2 = 2.905167809

Reorder the terms:
2.2 + x = 2.905167809

Solving
2.2 + x = 2.905167809

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = 2.905167809 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = 2.905167809 + -2.2
x = 2.905167809 + -2.2

Combine like terms: 2.905167809 + -2.2 = 0.705167809
x = 0.705167809

Simplifying
x = 0.705167809

Subproblem 2
x + 2.2 = -2.905167809

Simplifying
x + 2.2 = -2.905167809

Reorder the terms:
2.2 + x = -2.905167809

Solving
2.2 + x = -2.905167809

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = -2.905167809 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = -2.905167809 + -2.2
x = -2.905167809 + -2.2

Combine like terms: -2.905167809 + -2.2 = -5.105167809
x = -5.105167809

Simplifying
x = -5.105167809

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.705167809, -5.105167809}
Solution
x = {0.705167809, -5.105167809}