18x^2+60x+47=0

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Solution for 18x^2+60x+47=0 equation: 


Simplifying
18x2 + 60x + 47 = 0

Reorder the terms:
47 + 60x + 18x2 = 0

Solving
47 + 60x + 18x2 = 0

Solving for variable 'x'.

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

Divide each side by '18'.
2.611111111 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.611111111' to each side of the equation.
2.611111111 + 3.333333333x + -2.611111111 + x2 = 0 + -2.611111111

Reorder the terms:
2.611111111 + -2.611111111 + 3.333333333x + x2 = 0 + -2.611111111

Combine like terms: 2.611111111 + -2.611111111 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + -2.611111111
3.333333333x + x2 = 0 + -2.611111111

Combine like terms: 0 + -2.611111111 = -2.611111111
3.333333333x + x2 = -2.611111111

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -2.611111111 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -2.611111111 + 2.777777779

Combine like terms: -2.611111111 + 2.777777779 = 0.166666668
2.777777779 + 3.333333333x + x2 = 0.166666668

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 0.166666668

Calculate the square root of the right side: 0.408248292

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 0.408248292 and -0.408248292.


Subproblem 1
x + 1.666666667 = 0.408248292

Simplifying
x + 1.666666667 = 0.408248292

Reorder the terms:
1.666666667 + x = 0.408248292

Solving
1.666666667 + x = 0.408248292

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 0.408248292 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 0.408248292 + -1.666666667
x = 0.408248292 + -1.666666667

Combine like terms: 0.408248292 + -1.666666667 = -1.258418375
x = -1.258418375

Simplifying
x = -1.258418375


Subproblem 2
x + 1.666666667 = -0.408248292

Simplifying
x + 1.666666667 = -0.408248292

Reorder the terms:
1.666666667 + x = -0.408248292

Solving
1.666666667 + x = -0.408248292

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -0.408248292 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -0.408248292 + -1.666666667
x = -0.408248292 + -1.666666667

Combine like terms: -0.408248292 + -1.666666667 = -2.074914959
x = -2.074914959

Simplifying
x = -2.074914959


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.258418375, -2.074914959}

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