x^2+60x-600=0

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Solution for x^2+60x-600=0 equation: 


Simplifying
x2 + 60x + -600 = 0

Reorder the terms:
-600 + 60x + x2 = 0

Solving
-600 + 60x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '600' to each side of the equation.
-600 + 60x + 600 + x2 = 0 + 600

Reorder the terms:
-600 + 600 + 60x + x2 = 0 + 600

Combine like terms: -600 + 600 = 0
0 + 60x + x2 = 0 + 600
60x + x2 = 0 + 600

Combine like terms: 0 + 600 = 600
60x + x2 = 600

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 = 600 + 900

Reorder the terms:
900 + 60x + x2 = 600 + 900

Combine like terms: 600 + 900 = 1500
900 + 60x + x2 = 1500

Factor a perfect square on the left side:
(x + 30)(x + 30) = 1500

Calculate the square root of the right side: 38.729833462

Break this problem into two subproblems by setting 
(x + 30) equal to 38.729833462 and -38.729833462.


Subproblem 1
x + 30 = 38.729833462

Simplifying
x + 30 = 38.729833462

Reorder the terms:
30 + x = 38.729833462

Solving
30 + x = 38.729833462

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 = 38.729833462 + -30

Combine like terms: 30 + -30 = 0
0 + x = 38.729833462 + -30
x = 38.729833462 + -30

Combine like terms: 38.729833462 + -30 = 8.729833462
x = 8.729833462

Simplifying
x = 8.729833462


Subproblem 2
x + 30 = -38.729833462

Simplifying
x + 30 = -38.729833462

Reorder the terms:
30 + x = -38.729833462

Solving
30 + x = -38.729833462

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 = -38.729833462 + -30

Combine like terms: 30 + -30 = 0
0 + x = -38.729833462 + -30
x = -38.729833462 + -30

Combine like terms: -38.729833462 + -30 = -68.729833462
x = -68.729833462

Simplifying
x = -68.729833462


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.729833462, -68.729833462}

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