x^2+30x-480=0

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Solution for x^2+30x-480=0 equation: 


Simplifying
x2 + 30x + -480 = 0

Reorder the terms:
-480 + 30x + x2 = 0

Solving
-480 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '480' to each side of the equation.
-480 + 30x + 480 + x2 = 0 + 480

Reorder the terms:
-480 + 480 + 30x + x2 = 0 + 480

Combine like terms: -480 + 480 = 0
0 + 30x + x2 = 0 + 480
30x + x2 = 0 + 480

Combine like terms: 0 + 480 = 480
30x + x2 = 480

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 = 480 + 225

Reorder the terms:
225 + 30x + x2 = 480 + 225

Combine like terms: 480 + 225 = 705
225 + 30x + x2 = 705

Factor a perfect square on the left side:
(x + 15)(x + 15) = 705

Calculate the square root of the right side: 26.551836095

Break this problem into two subproblems by setting 
(x + 15) equal to 26.551836095 and -26.551836095.


Subproblem 1
x + 15 = 26.551836095

Simplifying
x + 15 = 26.551836095

Reorder the terms:
15 + x = 26.551836095

Solving
15 + x = 26.551836095

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 = 26.551836095 + -15

Combine like terms: 15 + -15 = 0
0 + x = 26.551836095 + -15
x = 26.551836095 + -15

Combine like terms: 26.551836095 + -15 = 11.551836095
x = 11.551836095

Simplifying
x = 11.551836095


Subproblem 2
x + 15 = -26.551836095

Simplifying
x + 15 = -26.551836095

Reorder the terms:
15 + x = -26.551836095

Solving
15 + x = -26.551836095

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 = -26.551836095 + -15

Combine like terms: 15 + -15 = 0
0 + x = -26.551836095 + -15
x = -26.551836095 + -15

Combine like terms: -26.551836095 + -15 = -41.551836095
x = -41.551836095

Simplifying
x = -41.551836095


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.551836095, -41.551836095}

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