x^2+60x-405=0

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Solution for x^2+60x-405=0 equation: 


Simplifying
x2 + 60x + -405 = 0

Reorder the terms:
-405 + 60x + x2 = 0

Solving
-405 + 60x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '405' to each side of the equation.
-405 + 60x + 405 + x2 = 0 + 405

Reorder the terms:
-405 + 405 + 60x + x2 = 0 + 405

Combine like terms: -405 + 405 = 0
0 + 60x + x2 = 0 + 405
60x + x2 = 0 + 405

Combine like terms: 0 + 405 = 405
60x + x2 = 405

The x term is 60x.  Take half its coefficient (30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
60x + 900 + x2 = 405 + 900

Reorder the terms:
900 + 60x + x2 = 405 + 900

Combine like terms: 405 + 900 = 1305
900 + 60x + x2 = 1305

Factor a perfect square on the left side:
(x + 30)(x + 30) = 1305

Calculate the square root of the right side: 36.124783736

Break this problem into two subproblems by setting 
(x + 30) equal to 36.124783736 and -36.124783736.


Subproblem 1
x + 30 = 36.124783736

Simplifying
x + 30 = 36.124783736

Reorder the terms:
30 + x = 36.124783736

Solving
30 + x = 36.124783736

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-30' to each side of the equation.
30 + -30 + x = 36.124783736 + -30

Combine like terms: 30 + -30 = 0
0 + x = 36.124783736 + -30
x = 36.124783736 + -30

Combine like terms: 36.124783736 + -30 = 6.124783736
x = 6.124783736

Simplifying
x = 6.124783736


Subproblem 2
x + 30 = -36.124783736

Simplifying
x + 30 = -36.124783736

Reorder the terms:
30 + x = -36.124783736

Solving
30 + x = -36.124783736

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-30' to each side of the equation.
30 + -30 + x = -36.124783736 + -30

Combine like terms: 30 + -30 = 0
0 + x = -36.124783736 + -30
x = -36.124783736 + -30

Combine like terms: -36.124783736 + -30 = -66.124783736
x = -66.124783736

Simplifying
x = -66.124783736


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.124783736, -66.124783736}

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