30x^2+95x-50=0

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Solution for 30x^2+95x-50=0 equation: 


Simplifying
30x2 + 95x + -50 = 0

Reorder the terms:
-50 + 95x + 30x2 = 0

Solving
-50 + 95x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + 19x + 6x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-10 + 19x + 6x2)' equal to zero and attempt to solve:

Simplifying
-10 + 19x + 6x2 = 0

Solving
-10 + 19x + 6x2 = 0

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

Divide each side by '6'.
-1.666666667 + 3.166666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 3.166666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 3.166666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 3.166666667x + x2 = 0 + 1.666666667
3.166666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
3.166666667x + x2 = 1.666666667

The x term is 3.166666667x.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667x + 2.506944447 + x2 = 1.666666667 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667x + x2 = 1.666666667 + 2.506944447

Combine like terms: 1.666666667 + 2.506944447 = 4.173611114
2.506944447 + 3.166666667x + x2 = 4.173611114

Factor a perfect square on the left side:
(x + 1.583333334)(x + 1.583333334) = 4.173611114

Calculate the square root of the right side: 2.042941779

Break this problem into two subproblems by setting 
(x + 1.583333334) equal to 2.042941779 and -2.042941779.


Subproblem 1
x + 1.583333334 = 2.042941779

Simplifying
x + 1.583333334 = 2.042941779

Reorder the terms:
1.583333334 + x = 2.042941779

Solving
1.583333334 + x = 2.042941779

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = 2.042941779 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = 2.042941779 + -1.583333334
x = 2.042941779 + -1.583333334

Combine like terms: 2.042941779 + -1.583333334 = 0.459608445
x = 0.459608445

Simplifying
x = 0.459608445


Subproblem 2
x + 1.583333334 = -2.042941779

Simplifying
x + 1.583333334 = -2.042941779

Reorder the terms:
1.583333334 + x = -2.042941779

Solving
1.583333334 + x = -2.042941779

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = -2.042941779 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = -2.042941779 + -1.583333334
x = -2.042941779 + -1.583333334

Combine like terms: -2.042941779 + -1.583333334 = -3.626275113
x = -3.626275113

Simplifying
x = -3.626275113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.459608445, -3.626275113}
Solution
x = {0.459608445, -3.626275113}

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