3x^2+15x-9.1=0

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Solution for 3x^2+15x-9.1=0 equation: 


Simplifying
3x2 + 15x + -9.1 = 0

Reorder the terms:
-9.1 + 15x + 3x2 = 0

Solving
-9.1 + 15x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-3.033333333 + 5x + x2 = 0

Move the constant term to the right:

Add '3.033333333' to each side of the equation.
-3.033333333 + 5x + 3.033333333 + x2 = 0 + 3.033333333

Reorder the terms:
-3.033333333 + 3.033333333 + 5x + x2 = 0 + 3.033333333

Combine like terms: -3.033333333 + 3.033333333 = 0.000000000
0.000000000 + 5x + x2 = 0 + 3.033333333
5x + x2 = 0 + 3.033333333

Combine like terms: 0 + 3.033333333 = 3.033333333
5x + x2 = 3.033333333

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 = 3.033333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 3.033333333 + 6.25

Combine like terms: 3.033333333 + 6.25 = 9.283333333
6.25 + 5x + x2 = 9.283333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 9.283333333

Calculate the square root of the right side: 3.046856303

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.046856303 and -3.046856303.


Subproblem 1
x + 2.5 = 3.046856303

Simplifying
x + 2.5 = 3.046856303

Reorder the terms:
2.5 + x = 3.046856303

Solving
2.5 + x = 3.046856303

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 = 3.046856303 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.046856303 + -2.5
x = 3.046856303 + -2.5

Combine like terms: 3.046856303 + -2.5 = 0.546856303
x = 0.546856303

Simplifying
x = 0.546856303


Subproblem 2
x + 2.5 = -3.046856303

Simplifying
x + 2.5 = -3.046856303

Reorder the terms:
2.5 + x = -3.046856303

Solving
2.5 + x = -3.046856303

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 = -3.046856303 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.046856303 + -2.5
x = -3.046856303 + -2.5

Combine like terms: -3.046856303 + -2.5 = -5.546856303
x = -5.546856303

Simplifying
x = -5.546856303


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.546856303, -5.546856303}

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