100x^2-230x+36=0

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Solution for 100x^2-230x+36=0 equation: 


Simplifying
100x2 + -230x + 36 = 0

Reorder the terms:
36 + -230x + 100x2 = 0

Solving
36 + -230x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -115x + 50x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + -115x + 50x2)' equal to zero and attempt to solve:

Simplifying
18 + -115x + 50x2 = 0

Solving
18 + -115x + 50x2 = 0

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

Divide each side by '50'.
0.36 + -2.3x + x2 = 0.0

Move the constant term to the right:

Add '-0.36' to each side of the equation.
0.36 + -2.3x + -0.36 + x2 = 0.0 + -0.36

Reorder the terms:
0.36 + -0.36 + -2.3x + x2 = 0.0 + -0.36

Combine like terms: 0.36 + -0.36 = 0.00
0.00 + -2.3x + x2 = 0.0 + -0.36
-2.3x + x2 = 0.0 + -0.36

Combine like terms: 0.0 + -0.36 = -0.36
-2.3x + x2 = -0.36

The x term is -2.3x.  Take half its coefficient (-1.15).
Square it (1.3225) and add it to both sides.

Add '1.3225' to each side of the equation.
-2.3x + 1.3225 + x2 = -0.36 + 1.3225

Reorder the terms:
1.3225 + -2.3x + x2 = -0.36 + 1.3225

Combine like terms: -0.36 + 1.3225 = 0.9625
1.3225 + -2.3x + x2 = 0.9625

Factor a perfect square on the left side:
(x + -1.15)(x + -1.15) = 0.9625

Calculate the square root of the right side: 0.981070844

Break this problem into two subproblems by setting 
(x + -1.15) equal to 0.981070844 and -0.981070844.


Subproblem 1
x + -1.15 = 0.981070844

Simplifying
x + -1.15 = 0.981070844

Reorder the terms:
-1.15 + x = 0.981070844

Solving
-1.15 + x = 0.981070844

Solving for variable 'x'.

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

Add '1.15' to each side of the equation.
-1.15 + 1.15 + x = 0.981070844 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + x = 0.981070844 + 1.15
x = 0.981070844 + 1.15

Combine like terms: 0.981070844 + 1.15 = 2.131070844
x = 2.131070844

Simplifying
x = 2.131070844


Subproblem 2
x + -1.15 = -0.981070844

Simplifying
x + -1.15 = -0.981070844

Reorder the terms:
-1.15 + x = -0.981070844

Solving
-1.15 + x = -0.981070844

Solving for variable 'x'.

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

Add '1.15' to each side of the equation.
-1.15 + 1.15 + x = -0.981070844 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + x = -0.981070844 + 1.15
x = -0.981070844 + 1.15

Combine like terms: -0.981070844 + 1.15 = 0.168929156
x = 0.168929156

Simplifying
x = 0.168929156


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.131070844, 0.168929156}
Solution
x = {2.131070844, 0.168929156}

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