30x^2-150x+100=0

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Solution for 30x^2-150x+100=0 equation: 


Simplifying
30x2 + -150x + 100 = 0

Reorder the terms:
100 + -150x + 30x2 = 0

Solving
100 + -150x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(10 + -15x + 3x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(10 + -15x + 3x2)' equal to zero and attempt to solve:

Simplifying
10 + -15x + 3x2 = 0

Solving
10 + -15x + 3x2 = 0

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

Divide each side by '3'.
3.333333333 + -5x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -5x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -5x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -5x + x2 = 0 + -3.333333333
-5x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-5x + x2 = -3.333333333

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 = -3.333333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3.333333333 + 6.25

Combine like terms: -3.333333333 + 6.25 = 2.916666667
6.25 + -5x + x2 = 2.916666667

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.707825128 and -1.707825128.


Subproblem 1
x + -2.5 = 1.707825128

Simplifying
x + -2.5 = 1.707825128

Reorder the terms:
-2.5 + x = 1.707825128

Solving
-2.5 + x = 1.707825128

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 = 1.707825128 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.707825128 + 2.5
x = 1.707825128 + 2.5

Combine like terms: 1.707825128 + 2.5 = 4.207825128
x = 4.207825128

Simplifying
x = 4.207825128


Subproblem 2
x + -2.5 = -1.707825128

Simplifying
x + -2.5 = -1.707825128

Reorder the terms:
-2.5 + x = -1.707825128

Solving
-2.5 + x = -1.707825128

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 = -1.707825128 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.707825128 + 2.5
x = -1.707825128 + 2.5

Combine like terms: -1.707825128 + 2.5 = 0.792174872
x = 0.792174872

Simplifying
x = 0.792174872


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.207825128, 0.792174872}
Solution
x = {4.207825128, 0.792174872}

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