25x^2-285x+100=0

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Solution for 25x^2-285x+100=0 equation: 


Simplifying
25x2 + -285x + 100 = 0

Reorder the terms:
100 + -285x + 25x2 = 0

Solving
100 + -285x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + -57x + 5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(20 + -57x + 5x2)' equal to zero and attempt to solve:

Simplifying
20 + -57x + 5x2 = 0

Solving
20 + -57x + 5x2 = 0

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

Divide each side by '5'.
4 + -11.4x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -11.4x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -11.4x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -11.4x + x2 = 0 + -4
-11.4x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-11.4x + x2 = -4

The x term is -11.4x.  Take half its coefficient (-5.7).
Square it (32.49) and add it to both sides.

Add '32.49' to each side of the equation.
-11.4x + 32.49 + x2 = -4 + 32.49

Reorder the terms:
32.49 + -11.4x + x2 = -4 + 32.49

Combine like terms: -4 + 32.49 = 28.49
32.49 + -11.4x + x2 = 28.49

Factor a perfect square on the left side:
(x + -5.7)(x + -5.7) = 28.49

Calculate the square root of the right side: 5.337602458

Break this problem into two subproblems by setting 
(x + -5.7) equal to 5.337602458 and -5.337602458.


Subproblem 1
x + -5.7 = 5.337602458

Simplifying
x + -5.7 = 5.337602458

Reorder the terms:
-5.7 + x = 5.337602458

Solving
-5.7 + x = 5.337602458

Solving for variable 'x'.

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

Add '5.7' to each side of the equation.
-5.7 + 5.7 + x = 5.337602458 + 5.7

Combine like terms: -5.7 + 5.7 = 0.0
0.0 + x = 5.337602458 + 5.7
x = 5.337602458 + 5.7

Combine like terms: 5.337602458 + 5.7 = 11.037602458
x = 11.037602458

Simplifying
x = 11.037602458


Subproblem 2
x + -5.7 = -5.337602458

Simplifying
x + -5.7 = -5.337602458

Reorder the terms:
-5.7 + x = -5.337602458

Solving
-5.7 + x = -5.337602458

Solving for variable 'x'.

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

Add '5.7' to each side of the equation.
-5.7 + 5.7 + x = -5.337602458 + 5.7

Combine like terms: -5.7 + 5.7 = 0.0
0.0 + x = -5.337602458 + 5.7
x = -5.337602458 + 5.7

Combine like terms: -5.337602458 + 5.7 = 0.362397542
x = 0.362397542

Simplifying
x = 0.362397542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.037602458, 0.362397542}
Solution
x = {11.037602458, 0.362397542}

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