9x(x)+27x+13=0

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Solution for 9x(x)+27x+13=0 equation:


Simplifying
9x(x) + 27x + 13 = 0

Multiply x * x
9x2 + 27x + 13 = 0

Reorder the terms:
13 + 27x + 9x2 = 0

Solving
13 + 27x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
1.444444444 + 3x + x2 = 0

Move the constant term to the right:

Add '-1.444444444' to each side of the equation.
1.444444444 + 3x + -1.444444444 + x2 = 0 + -1.444444444

Reorder the terms:
1.444444444 + -1.444444444 + 3x + x2 = 0 + -1.444444444

Combine like terms: 1.444444444 + -1.444444444 = 0.000000000
0.000000000 + 3x + x2 = 0 + -1.444444444
3x + x2 = 0 + -1.444444444

Combine like terms: 0 + -1.444444444 = -1.444444444
3x + x2 = -1.444444444

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -1.444444444 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -1.444444444 + 2.25

Combine like terms: -1.444444444 + 2.25 = 0.805555556
2.25 + 3x + x2 = 0.805555556

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 0.805555556

Calculate the square root of the right side: 0.897527468

Break this problem into two subproblems by setting 
(x + 1.5) equal to 0.897527468 and -0.897527468.

Subproblem 1

x + 1.5 = 0.897527468 Simplifying x + 1.5 = 0.897527468 Reorder the terms: 1.5 + x = 0.897527468 Solving 1.5 + x = 0.897527468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 0.897527468 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.897527468 + -1.5 x = 0.897527468 + -1.5 Combine like terms: 0.897527468 + -1.5 = -0.602472532 x = -0.602472532 Simplifying x = -0.602472532

Subproblem 2

x + 1.5 = -0.897527468 Simplifying x + 1.5 = -0.897527468 Reorder the terms: 1.5 + x = -0.897527468 Solving 1.5 + x = -0.897527468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -0.897527468 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.897527468 + -1.5 x = -0.897527468 + -1.5 Combine like terms: -0.897527468 + -1.5 = -2.397527468 x = -2.397527468 Simplifying x = -2.397527468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.602472532, -2.397527468}

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