-15x^2+100x-27=0

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Solution for -15x^2+100x-27=0 equation: 


Simplifying
-15x2 + 100x + -27 = 0

Reorder the terms:
-27 + 100x + -15x2 = 0

Solving
-27 + 100x + -15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
1.8 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + -6.666666667x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + -6.666666667x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + -6.666666667x + x2 = 0 + -1.8
-6.666666667x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
-6.666666667x + x2 = -1.8

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -1.8 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -1.8 + 11.11111112

Combine like terms: -1.8 + 11.11111112 = 9.31111112
11.11111112 + -6.666666667x + x2 = 9.31111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 9.31111112

Calculate the square root of the right side: 3.051411332

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 3.051411332 and -3.051411332.


Subproblem 1
x + -3.333333334 = 3.051411332

Simplifying
x + -3.333333334 = 3.051411332

Reorder the terms:
-3.333333334 + x = 3.051411332

Solving
-3.333333334 + x = 3.051411332

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 3.051411332 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 3.051411332 + 3.333333334
x = 3.051411332 + 3.333333334

Combine like terms: 3.051411332 + 3.333333334 = 6.384744666
x = 6.384744666

Simplifying
x = 6.384744666


Subproblem 2
x + -3.333333334 = -3.051411332

Simplifying
x + -3.333333334 = -3.051411332

Reorder the terms:
-3.333333334 + x = -3.051411332

Solving
-3.333333334 + x = -3.051411332

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -3.051411332 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -3.051411332 + 3.333333334
x = -3.051411332 + 3.333333334

Combine like terms: -3.051411332 + 3.333333334 = 0.281922002
x = 0.281922002

Simplifying
x = 0.281922002


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.384744666, 0.281922002}

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