100=15X^2-5X

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Solution for 100=15X^2-5X equation: 


Simplifying
100 = 15X2 + -5X

Reorder the terms:
100 = -5X + 15X2

Solving
100 = -5X + 15X2

Solving for variable 'X'.

Reorder the terms:
100 + 5X + -15X2 = -5X + 5X + 15X2 + -15X2

Combine like terms: -5X + 5X = 0
100 + 5X + -15X2 = 0 + 15X2 + -15X2
100 + 5X + -15X2 = 15X2 + -15X2

Combine like terms: 15X2 + -15X2 = 0
100 + 5X + -15X2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + X + -3X2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(20 + X + -3X2)' equal to zero and attempt to solve:

Simplifying
20 + X + -3X2 = 0

Solving
20 + X + -3X2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-6.666666667 + -0.3333333333X + X2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -0.3333333333X + 6.666666667 + X2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -0.3333333333X + X2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -0.3333333333X + X2 = 0 + 6.666666667
-0.3333333333X + X2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-0.3333333333X + X2 = 6.666666667

The X term is X.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.3333333333X + 0.25 + X2 = 6.666666667 + 0.25

Reorder the terms:
0.25 + -0.3333333333X + X2 = 6.666666667 + 0.25

Combine like terms: 6.666666667 + 0.25 = 6.916666667
0.25 + -0.3333333333X + X2 = 6.916666667

Factor a perfect square on the left side:
(X + 0.5)(X + 0.5) = 6.916666667

Calculate the square root of the right side: 2.62995564

Break this problem into two subproblems by setting 
(X + 0.5) equal to 2.62995564 and -2.62995564.


Subproblem 1
X + 0.5 = 2.62995564

Simplifying
X + 0.5 = 2.62995564

Reorder the terms:
0.5 + X = 2.62995564

Solving
0.5 + X = 2.62995564

Solving for variable 'X'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + X = 2.62995564 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = 2.62995564 + -0.5
X = 2.62995564 + -0.5

Combine like terms: 2.62995564 + -0.5 = 2.12995564
X = 2.12995564

Simplifying
X = 2.12995564


Subproblem 2
X + 0.5 = -2.62995564

Simplifying
X + 0.5 = -2.62995564

Reorder the terms:
0.5 + X = -2.62995564

Solving
0.5 + X = -2.62995564

Solving for variable 'X'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + X = -2.62995564 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = -2.62995564 + -0.5
X = -2.62995564 + -0.5

Combine like terms: -2.62995564 + -0.5 = -3.12995564
X = -3.12995564

Simplifying
X = -3.12995564


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.12995564, -3.12995564}
Solution
X = {2.12995564, -3.12995564}

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