x^2+30x+198=0

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Solution for x^2+30x+198=0 equation: 


Simplifying
x2 + 30x + 198 = 0

Reorder the terms:
198 + 30x + x2 = 0

Solving
198 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-198' to each side of the equation.
198 + 30x + -198 + x2 = 0 + -198

Reorder the terms:
198 + -198 + 30x + x2 = 0 + -198

Combine like terms: 198 + -198 = 0
0 + 30x + x2 = 0 + -198
30x + x2 = 0 + -198

Combine like terms: 0 + -198 = -198
30x + x2 = -198

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -198 + 225

Reorder the terms:
225 + 30x + x2 = -198 + 225

Combine like terms: -198 + 225 = 27
225 + 30x + x2 = 27

Factor a perfect square on the left side:
(x + 15)(x + 15) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + 15) equal to 5.196152423 and -5.196152423.


Subproblem 1
x + 15 = 5.196152423

Simplifying
x + 15 = 5.196152423

Reorder the terms:
15 + x = 5.196152423

Solving
15 + x = 5.196152423

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 5.196152423 + -15

Combine like terms: 15 + -15 = 0
0 + x = 5.196152423 + -15
x = 5.196152423 + -15

Combine like terms: 5.196152423 + -15 = -9.803847577
x = -9.803847577

Simplifying
x = -9.803847577


Subproblem 2
x + 15 = -5.196152423

Simplifying
x + 15 = -5.196152423

Reorder the terms:
15 + x = -5.196152423

Solving
15 + x = -5.196152423

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -5.196152423 + -15

Combine like terms: 15 + -15 = 0
0 + x = -5.196152423 + -15
x = -5.196152423 + -15

Combine like terms: -5.196152423 + -15 = -20.196152423
x = -20.196152423

Simplifying
x = -20.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-9.803847577, -20.196152423}

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