x^2+30x+114=0

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Solution for x^2+30x+114=0 equation: 


Simplifying
x2 + 30x + 114 = 0

Reorder the terms:
114 + 30x + x2 = 0

Solving
114 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-114' to each side of the equation.
114 + 30x + -114 + x2 = 0 + -114

Reorder the terms:
114 + -114 + 30x + x2 = 0 + -114

Combine like terms: 114 + -114 = 0
0 + 30x + x2 = 0 + -114
30x + x2 = 0 + -114

Combine like terms: 0 + -114 = -114
30x + x2 = -114

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 = -114 + 225

Reorder the terms:
225 + 30x + x2 = -114 + 225

Combine like terms: -114 + 225 = 111
225 + 30x + x2 = 111

Factor a perfect square on the left side:
(x + 15)(x + 15) = 111

Calculate the square root of the right side: 10.535653753

Break this problem into two subproblems by setting 
(x + 15) equal to 10.535653753 and -10.535653753.


Subproblem 1
x + 15 = 10.535653753

Simplifying
x + 15 = 10.535653753

Reorder the terms:
15 + x = 10.535653753

Solving
15 + x = 10.535653753

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 = 10.535653753 + -15

Combine like terms: 15 + -15 = 0
0 + x = 10.535653753 + -15
x = 10.535653753 + -15

Combine like terms: 10.535653753 + -15 = -4.464346247
x = -4.464346247

Simplifying
x = -4.464346247


Subproblem 2
x + 15 = -10.535653753

Simplifying
x + 15 = -10.535653753

Reorder the terms:
15 + x = -10.535653753

Solving
15 + x = -10.535653753

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 = -10.535653753 + -15

Combine like terms: 15 + -15 = 0
0 + x = -10.535653753 + -15
x = -10.535653753 + -15

Combine like terms: -10.535653753 + -15 = -25.535653753
x = -25.535653753

Simplifying
x = -25.535653753


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.464346247, -25.535653753}

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