-2.7x^2+35x-3=0

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Solution for -2.7x^2+35x-3=0 equation: 


Simplifying
-2.7x2 + 35x + -3 = 0

Reorder the terms:
-3 + 35x + -2.7x2 = 0

Solving
-3 + 35x + -2.7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2.7 the coefficient of the squared term: 

Divide each side by '-2.7'.
1.111111111 + -12.96296296x + x2 = 0

Move the constant term to the right:

Add '-1.111111111' to each side of the equation.
1.111111111 + -12.96296296x + -1.111111111 + x2 = 0 + -1.111111111

Reorder the terms:
1.111111111 + -1.111111111 + -12.96296296x + x2 = 0 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + -12.96296296x + x2 = 0 + -1.111111111
-12.96296296x + x2 = 0 + -1.111111111

Combine like terms: 0 + -1.111111111 = -1.111111111
-12.96296296x + x2 = -1.111111111

The x term is -12.96296296x.  Take half its coefficient (-6.48148148).
Square it (42.00960218) and add it to both sides.

Add '42.00960218' to each side of the equation.
-12.96296296x + 42.00960218 + x2 = -1.111111111 + 42.00960218

Reorder the terms:
42.00960218 + -12.96296296x + x2 = -1.111111111 + 42.00960218

Combine like terms: -1.111111111 + 42.00960218 = 40.898491069
42.00960218 + -12.96296296x + x2 = 40.898491069

Factor a perfect square on the left side:
(x + -6.48148148)(x + -6.48148148) = 40.898491069

Calculate the square root of the right side: 6.395192809

Break this problem into two subproblems by setting 
(x + -6.48148148) equal to 6.395192809 and -6.395192809.


Subproblem 1
x + -6.48148148 = 6.395192809

Simplifying
x + -6.48148148 = 6.395192809

Reorder the terms:
-6.48148148 + x = 6.395192809

Solving
-6.48148148 + x = 6.395192809

Solving for variable 'x'.

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

Add '6.48148148' to each side of the equation.
-6.48148148 + 6.48148148 + x = 6.395192809 + 6.48148148

Combine like terms: -6.48148148 + 6.48148148 = 0.00000000
0.00000000 + x = 6.395192809 + 6.48148148
x = 6.395192809 + 6.48148148

Combine like terms: 6.395192809 + 6.48148148 = 12.876674289
x = 12.876674289

Simplifying
x = 12.876674289


Subproblem 2
x + -6.48148148 = -6.395192809

Simplifying
x + -6.48148148 = -6.395192809

Reorder the terms:
-6.48148148 + x = -6.395192809

Solving
-6.48148148 + x = -6.395192809

Solving for variable 'x'.

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

Add '6.48148148' to each side of the equation.
-6.48148148 + 6.48148148 + x = -6.395192809 + 6.48148148

Combine like terms: -6.48148148 + 6.48148148 = 0.00000000
0.00000000 + x = -6.395192809 + 6.48148148
x = -6.395192809 + 6.48148148

Combine like terms: -6.395192809 + 6.48148148 = 0.086288671
x = 0.086288671

Simplifying
x = 0.086288671


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.876674289, 0.086288671}

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