3x^2+27x-9.1=0

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Solution for 3x^2+27x-9.1=0 equation:


Simplifying
3x2 + 27x + -9.1 = 0

Reorder the terms:
-9.1 + 27x + 3x2 = 0

Solving
-9.1 + 27x + 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 + 9x + x2 = 0

Move the constant term to the right:

Add '3.033333333' to each side of the equation.
-3.033333333 + 9x + 3.033333333 + x2 = 0 + 3.033333333

Reorder the terms:
-3.033333333 + 3.033333333 + 9x + x2 = 0 + 3.033333333

Combine like terms: -3.033333333 + 3.033333333 = 0.000000000
0.000000000 + 9x + x2 = 0 + 3.033333333
9x + x2 = 0 + 3.033333333

Combine like terms: 0 + 3.033333333 = 3.033333333
9x + x2 = 3.033333333

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 3.033333333 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 3.033333333 + 20.25

Combine like terms: 3.033333333 + 20.25 = 23.283333333
20.25 + 9x + x2 = 23.283333333

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 23.283333333

Calculate the square root of the right side: 4.825280648

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.825280648 and -4.825280648.

Subproblem 1

x + 4.5 = 4.825280648 Simplifying x + 4.5 = 4.825280648 Reorder the terms: 4.5 + x = 4.825280648 Solving 4.5 + x = 4.825280648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.825280648 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.825280648 + -4.5 x = 4.825280648 + -4.5 Combine like terms: 4.825280648 + -4.5 = 0.325280648 x = 0.325280648 Simplifying x = 0.325280648

Subproblem 2

x + 4.5 = -4.825280648 Simplifying x + 4.5 = -4.825280648 Reorder the terms: 4.5 + x = -4.825280648 Solving 4.5 + x = -4.825280648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.825280648 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.825280648 + -4.5 x = -4.825280648 + -4.5 Combine like terms: -4.825280648 + -4.5 = -9.325280648 x = -9.325280648 Simplifying x = -9.325280648

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.325280648, -9.325280648}

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