x^2+30x+110=0

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Solution for x^2+30x+110=0 equation: 


Simplifying
x2 + 30x + 110 = 0

Reorder the terms:
110 + 30x + x2 = 0

Solving
110 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-110' to each side of the equation.
110 + 30x + -110 + x2 = 0 + -110

Reorder the terms:
110 + -110 + 30x + x2 = 0 + -110

Combine like terms: 110 + -110 = 0
0 + 30x + x2 = 0 + -110
30x + x2 = 0 + -110

Combine like terms: 0 + -110 = -110
30x + x2 = -110

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 = -110 + 225

Reorder the terms:
225 + 30x + x2 = -110 + 225

Combine like terms: -110 + 225 = 115
225 + 30x + x2 = 115

Factor a perfect square on the left side:
(x + 15)(x + 15) = 115

Calculate the square root of the right side: 10.723805295

Break this problem into two subproblems by setting 
(x + 15) equal to 10.723805295 and -10.723805295.


Subproblem 1
x + 15 = 10.723805295

Simplifying
x + 15 = 10.723805295

Reorder the terms:
15 + x = 10.723805295

Solving
15 + x = 10.723805295

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 = 10.723805295 + -15

Combine like terms: 15 + -15 = 0
0 + x = 10.723805295 + -15
x = 10.723805295 + -15

Combine like terms: 10.723805295 + -15 = -4.276194705
x = -4.276194705

Simplifying
x = -4.276194705


Subproblem 2
x + 15 = -10.723805295

Simplifying
x + 15 = -10.723805295

Reorder the terms:
15 + x = -10.723805295

Solving
15 + x = -10.723805295

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 = -10.723805295 + -15

Combine like terms: 15 + -15 = 0
0 + x = -10.723805295 + -15
x = -10.723805295 + -15

Combine like terms: -10.723805295 + -15 = -25.723805295
x = -25.723805295

Simplifying
x = -25.723805295


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.276194705, -25.723805295}

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