15x^2-10x-100=0

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Solution for 15x^2-10x-100=0 equation: 


Simplifying
15x2 + -10x + -100 = 0

Reorder the terms:
-100 + -10x + 15x2 = 0

Solving
-100 + -10x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + -2x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-20 + -2x + 3x2)' equal to zero and attempt to solve:

Simplifying
-20 + -2x + 3x2 = 0

Solving
-20 + -2x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -0.6666666667x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -0.6666666667x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 6.666666667
-0.6666666667x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-0.6666666667x + x2 = 6.666666667

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 6.666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 6.666666667 + 0.1111111112

Combine like terms: 6.666666667 + 0.1111111112 = 6.7777777782
0.1111111112 + -0.6666666667x + x2 = 6.7777777782

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 6.7777777782

Calculate the square root of the right side: 2.603416559

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 2.603416559 and -2.603416559.


Subproblem 1
x + -0.3333333334 = 2.603416559

Simplifying
x + -0.3333333334 = 2.603416559

Reorder the terms:
-0.3333333334 + x = 2.603416559

Solving
-0.3333333334 + x = 2.603416559

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 2.603416559 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 2.603416559 + 0.3333333334
x = 2.603416559 + 0.3333333334

Combine like terms: 2.603416559 + 0.3333333334 = 2.9367498924
x = 2.9367498924

Simplifying
x = 2.9367498924


Subproblem 2
x + -0.3333333334 = -2.603416559

Simplifying
x + -0.3333333334 = -2.603416559

Reorder the terms:
-0.3333333334 + x = -2.603416559

Solving
-0.3333333334 + x = -2.603416559

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -2.603416559 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -2.603416559 + 0.3333333334
x = -2.603416559 + 0.3333333334

Combine like terms: -2.603416559 + 0.3333333334 = -2.2700832256
x = -2.2700832256

Simplifying
x = -2.2700832256


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.9367498924, -2.2700832256}
Solution
x = {2.9367498924, -2.2700832256}

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