5x^2+27x+18=0

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Solution for 5x^2+27x+18=0 equation:


Simplifying
5x2 + 27x + 18 = 0

Reorder the terms:
18 + 27x + 5x2 = 0

Solving
18 + 27x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
3.6 + 5.4x + x2 = 0

Move the constant term to the right:

Add '-3.6' to each side of the equation.
3.6 + 5.4x + -3.6 + x2 = 0 + -3.6

Reorder the terms:
3.6 + -3.6 + 5.4x + x2 = 0 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + 5.4x + x2 = 0 + -3.6
5.4x + x2 = 0 + -3.6

Combine like terms: 0 + -3.6 = -3.6
5.4x + x2 = -3.6

The x term is 5.4x.  Take half its coefficient (2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
5.4x + 7.29 + x2 = -3.6 + 7.29

Reorder the terms:
7.29 + 5.4x + x2 = -3.6 + 7.29

Combine like terms: -3.6 + 7.29 = 3.69
7.29 + 5.4x + x2 = 3.69

Factor a perfect square on the left side:
(x + 2.7)(x + 2.7) = 3.69

Calculate the square root of the right side: 1.920937271

Break this problem into two subproblems by setting 
(x + 2.7) equal to 1.920937271 and -1.920937271.

Subproblem 1

x + 2.7 = 1.920937271 Simplifying x + 2.7 = 1.920937271 Reorder the terms: 2.7 + x = 1.920937271 Solving 2.7 + x = 1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = 1.920937271 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 1.920937271 + -2.7 x = 1.920937271 + -2.7 Combine like terms: 1.920937271 + -2.7 = -0.779062729 x = -0.779062729 Simplifying x = -0.779062729

Subproblem 2

x + 2.7 = -1.920937271 Simplifying x + 2.7 = -1.920937271 Reorder the terms: 2.7 + x = -1.920937271 Solving 2.7 + x = -1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = -1.920937271 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -1.920937271 + -2.7 x = -1.920937271 + -2.7 Combine like terms: -1.920937271 + -2.7 = -4.620937271 x = -4.620937271 Simplifying x = -4.620937271

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.779062729, -4.620937271}

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