9x^2+30x-47=0

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Solution for 9x^2+30x-47=0 equation: 


Simplifying
9x2 + 30x + -47 = 0

Reorder the terms:
-47 + 30x + 9x2 = 0

Solving
-47 + 30x + 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'.
-5.222222222 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '5.222222222' to each side of the equation.
-5.222222222 + 3.333333333x + 5.222222222 + x2 = 0 + 5.222222222

Reorder the terms:
-5.222222222 + 5.222222222 + 3.333333333x + x2 = 0 + 5.222222222

Combine like terms: -5.222222222 + 5.222222222 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + 5.222222222
3.333333333x + x2 = 0 + 5.222222222

Combine like terms: 0 + 5.222222222 = 5.222222222
3.333333333x + x2 = 5.222222222

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 = 5.222222222 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 5.222222222 + 2.777777779

Combine like terms: 5.222222222 + 2.777777779 = 8.000000001
2.777777779 + 3.333333333x + x2 = 8.000000001

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 8.000000001

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + 1.666666667 = 2.828427125

Simplifying
x + 1.666666667 = 2.828427125

Reorder the terms:
1.666666667 + x = 2.828427125

Solving
1.666666667 + x = 2.828427125

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 = 2.828427125 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 2.828427125 + -1.666666667
x = 2.828427125 + -1.666666667

Combine like terms: 2.828427125 + -1.666666667 = 1.161760458
x = 1.161760458

Simplifying
x = 1.161760458


Subproblem 2
x + 1.666666667 = -2.828427125

Simplifying
x + 1.666666667 = -2.828427125

Reorder the terms:
1.666666667 + x = -2.828427125

Solving
1.666666667 + x = -2.828427125

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 = -2.828427125 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -2.828427125 + -1.666666667
x = -2.828427125 + -1.666666667

Combine like terms: -2.828427125 + -1.666666667 = -4.495093792
x = -4.495093792

Simplifying
x = -4.495093792


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.161760458, -4.495093792}

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