25x^2-20x-50=0

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Solution for 25x^2-20x-50=0 equation: 


Simplifying
25x2 + -20x + -50 = 0

Reorder the terms:
-50 + -20x + 25x2 = 0

Solving
-50 + -20x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + -4x + 5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-10 + -4x + 5x2)' equal to zero and attempt to solve:

Simplifying
-10 + -4x + 5x2 = 0

Solving
-10 + -4x + 5x2 = 0

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

Divide each side by '5'.
-2 + -0.8x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.8x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.8x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.8x + x2 = 0 + 2
-0.8x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.8x + x2 = 2

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 2 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 2 + 0.16

Combine like terms: 2 + 0.16 = 2.16
0.16 + -0.8x + x2 = 2.16

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 2.16

Calculate the square root of the right side: 1.469693846

Break this problem into two subproblems by setting 
(x + -0.4) equal to 1.469693846 and -1.469693846.


Subproblem 1
x + -0.4 = 1.469693846

Simplifying
x + -0.4 = 1.469693846

Reorder the terms:
-0.4 + x = 1.469693846

Solving
-0.4 + x = 1.469693846

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 1.469693846 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 1.469693846 + 0.4
x = 1.469693846 + 0.4

Combine like terms: 1.469693846 + 0.4 = 1.869693846
x = 1.869693846

Simplifying
x = 1.869693846


Subproblem 2
x + -0.4 = -1.469693846

Simplifying
x + -0.4 = -1.469693846

Reorder the terms:
-0.4 + x = -1.469693846

Solving
-0.4 + x = -1.469693846

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -1.469693846 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -1.469693846 + 0.4
x = -1.469693846 + 0.4

Combine like terms: -1.469693846 + 0.4 = -1.069693846
x = -1.069693846

Simplifying
x = -1.069693846


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.869693846, -1.069693846}
Solution
x = {1.869693846, -1.069693846}

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