9x^2+30x-55=0

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Solution for 9x^2+30x-55=0 equation: 


Simplifying
9x2 + 30x + -55 = 0

Reorder the terms:
-55 + 30x + 9x2 = 0

Solving
-55 + 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'.
-6.111111111 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '6.111111111' to each side of the equation.
-6.111111111 + 3.333333333x + 6.111111111 + x2 = 0 + 6.111111111

Reorder the terms:
-6.111111111 + 6.111111111 + 3.333333333x + x2 = 0 + 6.111111111

Combine like terms: -6.111111111 + 6.111111111 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + 6.111111111
3.333333333x + x2 = 0 + 6.111111111

Combine like terms: 0 + 6.111111111 = 6.111111111
3.333333333x + x2 = 6.111111111

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 = 6.111111111 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 6.111111111 + 2.777777779

Combine like terms: 6.111111111 + 2.777777779 = 8.88888889
2.777777779 + 3.333333333x + x2 = 8.88888889

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 8.88888889

Calculate the square root of the right side: 2.98142397

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 2.98142397 and -2.98142397.


Subproblem 1
x + 1.666666667 = 2.98142397

Simplifying
x + 1.666666667 = 2.98142397

Reorder the terms:
1.666666667 + x = 2.98142397

Solving
1.666666667 + x = 2.98142397

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 = 2.98142397 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 2.98142397 + -1.666666667
x = 2.98142397 + -1.666666667

Combine like terms: 2.98142397 + -1.666666667 = 1.314757303
x = 1.314757303

Simplifying
x = 1.314757303


Subproblem 2
x + 1.666666667 = -2.98142397

Simplifying
x + 1.666666667 = -2.98142397

Reorder the terms:
1.666666667 + x = -2.98142397

Solving
1.666666667 + x = -2.98142397

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 = -2.98142397 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -2.98142397 + -1.666666667
x = -2.98142397 + -1.666666667

Combine like terms: -2.98142397 + -1.666666667 = -4.648090637
x = -4.648090637

Simplifying
x = -4.648090637


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.314757303, -4.648090637}

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