100x^2-500x+625=40

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Solution for 100x^2-500x+625=40 equation: 


Simplifying
100x2 + -500x + 625 = 40

Reorder the terms:
625 + -500x + 100x2 = 40

Solving
625 + -500x + 100x2 = 40

Solving for variable 'x'.

Reorder the terms:
625 + -40 + -500x + 100x2 = 40 + -40

Combine like terms: 625 + -40 = 585
585 + -500x + 100x2 = 40 + -40

Combine like terms: 40 + -40 = 0
585 + -500x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(117 + -100x + 20x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(117 + -100x + 20x2)' equal to zero and attempt to solve:

Simplifying
117 + -100x + 20x2 = 0

Solving
117 + -100x + 20x2 = 0

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

Divide each side by '20'.
5.85 + -5x + x2 = 0.0

Move the constant term to the right:

Add '-5.85' to each side of the equation.
5.85 + -5x + -5.85 + x2 = 0.0 + -5.85

Reorder the terms:
5.85 + -5.85 + -5x + x2 = 0.0 + -5.85

Combine like terms: 5.85 + -5.85 = 0.00
0.00 + -5x + x2 = 0.0 + -5.85
-5x + x2 = 0.0 + -5.85

Combine like terms: 0.0 + -5.85 = -5.85
-5x + x2 = -5.85

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -5.85 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -5.85 + 6.25

Combine like terms: -5.85 + 6.25 = 0.4
6.25 + -5x + x2 = 0.4

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(x + -2.5) equal to 0.632455532 and -0.632455532.


Subproblem 1
x + -2.5 = 0.632455532

Simplifying
x + -2.5 = 0.632455532

Reorder the terms:
-2.5 + x = 0.632455532

Solving
-2.5 + x = 0.632455532

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 0.632455532 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 0.632455532 + 2.5
x = 0.632455532 + 2.5

Combine like terms: 0.632455532 + 2.5 = 3.132455532
x = 3.132455532

Simplifying
x = 3.132455532


Subproblem 2
x + -2.5 = -0.632455532

Simplifying
x + -2.5 = -0.632455532

Reorder the terms:
-2.5 + x = -0.632455532

Solving
-2.5 + x = -0.632455532

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -0.632455532 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -0.632455532 + 2.5
x = -0.632455532 + 2.5

Combine like terms: -0.632455532 + 2.5 = 1.867544468
x = 1.867544468

Simplifying
x = 1.867544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.132455532, 1.867544468}
Solution
x = {3.132455532, 1.867544468}

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