x^2+30x+181=0

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Solution for x^2+30x+181=0 equation: 


Simplifying
x2 + 30x + 181 = 0

Reorder the terms:
181 + 30x + x2 = 0

Solving
181 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-181' to each side of the equation.
181 + 30x + -181 + x2 = 0 + -181

Reorder the terms:
181 + -181 + 30x + x2 = 0 + -181

Combine like terms: 181 + -181 = 0
0 + 30x + x2 = 0 + -181
30x + x2 = 0 + -181

Combine like terms: 0 + -181 = -181
30x + x2 = -181

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 = -181 + 225

Reorder the terms:
225 + 30x + x2 = -181 + 225

Combine like terms: -181 + 225 = 44
225 + 30x + x2 = 44

Factor a perfect square on the left side:
(x + 15)(x + 15) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + 15) equal to 6.633249581 and -6.633249581.


Subproblem 1
x + 15 = 6.633249581

Simplifying
x + 15 = 6.633249581

Reorder the terms:
15 + x = 6.633249581

Solving
15 + x = 6.633249581

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 = 6.633249581 + -15

Combine like terms: 15 + -15 = 0
0 + x = 6.633249581 + -15
x = 6.633249581 + -15

Combine like terms: 6.633249581 + -15 = -8.366750419
x = -8.366750419

Simplifying
x = -8.366750419


Subproblem 2
x + 15 = -6.633249581

Simplifying
x + 15 = -6.633249581

Reorder the terms:
15 + x = -6.633249581

Solving
15 + x = -6.633249581

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 = -6.633249581 + -15

Combine like terms: 15 + -15 = 0
0 + x = -6.633249581 + -15
x = -6.633249581 + -15

Combine like terms: -6.633249581 + -15 = -21.633249581
x = -21.633249581

Simplifying
x = -21.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.366750419, -21.633249581}

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