x^2+60x-2801=0

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Solution for x^2+60x-2801=0 equation: 


Simplifying
x2 + 60x + -2801 = 0

Reorder the terms:
-2801 + 60x + x2 = 0

Solving
-2801 + 60x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2801' to each side of the equation.
-2801 + 60x + 2801 + x2 = 0 + 2801

Reorder the terms:
-2801 + 2801 + 60x + x2 = 0 + 2801

Combine like terms: -2801 + 2801 = 0
0 + 60x + x2 = 0 + 2801
60x + x2 = 0 + 2801

Combine like terms: 0 + 2801 = 2801
60x + x2 = 2801

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 = 2801 + 900

Reorder the terms:
900 + 60x + x2 = 2801 + 900

Combine like terms: 2801 + 900 = 3701
900 + 60x + x2 = 3701

Factor a perfect square on the left side:
(x + 30)(x + 30) = 3701

Calculate the square root of the right side: 60.835844697

Break this problem into two subproblems by setting 
(x + 30) equal to 60.835844697 and -60.835844697.


Subproblem 1
x + 30 = 60.835844697

Simplifying
x + 30 = 60.835844697

Reorder the terms:
30 + x = 60.835844697

Solving
30 + x = 60.835844697

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 = 60.835844697 + -30

Combine like terms: 30 + -30 = 0
0 + x = 60.835844697 + -30
x = 60.835844697 + -30

Combine like terms: 60.835844697 + -30 = 30.835844697
x = 30.835844697

Simplifying
x = 30.835844697


Subproblem 2
x + 30 = -60.835844697

Simplifying
x + 30 = -60.835844697

Reorder the terms:
30 + x = -60.835844697

Solving
30 + x = -60.835844697

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 = -60.835844697 + -30

Combine like terms: 30 + -30 = 0
0 + x = -60.835844697 + -30
x = -60.835844697 + -30

Combine like terms: -60.835844697 + -30 = -90.835844697
x = -90.835844697

Simplifying
x = -90.835844697


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.835844697, -90.835844697}

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