x^2+30x+102=0

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Solution for x^2+30x+102=0 equation: 


Simplifying
x2 + 30x + 102 = 0

Reorder the terms:
102 + 30x + x2 = 0

Solving
102 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-102' to each side of the equation.
102 + 30x + -102 + x2 = 0 + -102

Reorder the terms:
102 + -102 + 30x + x2 = 0 + -102

Combine like terms: 102 + -102 = 0
0 + 30x + x2 = 0 + -102
30x + x2 = 0 + -102

Combine like terms: 0 + -102 = -102
30x + x2 = -102

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 = -102 + 225

Reorder the terms:
225 + 30x + x2 = -102 + 225

Combine like terms: -102 + 225 = 123
225 + 30x + x2 = 123

Factor a perfect square on the left side:
(x + 15)(x + 15) = 123

Calculate the square root of the right side: 11.090536506

Break this problem into two subproblems by setting 
(x + 15) equal to 11.090536506 and -11.090536506.


Subproblem 1
x + 15 = 11.090536506

Simplifying
x + 15 = 11.090536506

Reorder the terms:
15 + x = 11.090536506

Solving
15 + x = 11.090536506

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 = 11.090536506 + -15

Combine like terms: 15 + -15 = 0
0 + x = 11.090536506 + -15
x = 11.090536506 + -15

Combine like terms: 11.090536506 + -15 = -3.909463494
x = -3.909463494

Simplifying
x = -3.909463494


Subproblem 2
x + 15 = -11.090536506

Simplifying
x + 15 = -11.090536506

Reorder the terms:
15 + x = -11.090536506

Solving
15 + x = -11.090536506

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 = -11.090536506 + -15

Combine like terms: 15 + -15 = 0
0 + x = -11.090536506 + -15
x = -11.090536506 + -15

Combine like terms: -11.090536506 + -15 = -26.090536506
x = -26.090536506

Simplifying
x = -26.090536506


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.909463494, -26.090536506}

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