25x^2-15x-20=0

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Solution for 25x^2-15x-20=0 equation: 


Simplifying
25x2 + -15x + -20 = 0

Reorder the terms:
-20 + -15x + 25x2 = 0

Solving
-20 + -15x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + -3x + 5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + -3x + 5x2)' equal to zero and attempt to solve:

Simplifying
-4 + -3x + 5x2 = 0

Solving
-4 + -3x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + -0.6x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -0.6x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -0.6x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -0.6x + x2 = 0 + 0.8
-0.6x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-0.6x + x2 = 0.8

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 0.8 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 0.8 + 0.09

Combine like terms: 0.8 + 0.09 = 0.89
0.09 + -0.6x + x2 = 0.89

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.89

Calculate the square root of the right side: 0.943398113

Break this problem into two subproblems by setting 
(x + -0.3) equal to 0.943398113 and -0.943398113.


Subproblem 1
x + -0.3 = 0.943398113

Simplifying
x + -0.3 = 0.943398113

Reorder the terms:
-0.3 + x = 0.943398113

Solving
-0.3 + x = 0.943398113

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 0.943398113 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 0.943398113 + 0.3
x = 0.943398113 + 0.3

Combine like terms: 0.943398113 + 0.3 = 1.243398113
x = 1.243398113

Simplifying
x = 1.243398113


Subproblem 2
x + -0.3 = -0.943398113

Simplifying
x + -0.3 = -0.943398113

Reorder the terms:
-0.3 + x = -0.943398113

Solving
-0.3 + x = -0.943398113

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -0.943398113 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -0.943398113 + 0.3
x = -0.943398113 + 0.3

Combine like terms: -0.943398113 + 0.3 = -0.643398113
x = -0.643398113

Simplifying
x = -0.643398113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.243398113, -0.643398113}
Solution
x = {1.243398113, -0.643398113}

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