(-1x^2)-21x-60=0

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Solution for (-1x^2)-21x-60=0 equation: 


Simplifying
(-1x2) + -21x + -60 = 0

Reorder the terms:
-60 + -21x + (-1x2) = 0

Solving
-60 + -21x + (-1x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(60 + 21x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(60 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
60 + 21x + x2 = 0

Solving
60 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + 21x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + 21x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 21x + x2 = 0 + -60
21x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
21x + x2 = -60

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -60 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -60 + 110.25

Combine like terms: -60 + 110.25 = 50.25
110.25 + 21x + x2 = 50.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + 10.5) equal to 7.088723439 and -7.088723439.


Subproblem 1
x + 10.5 = 7.088723439

Simplifying
x + 10.5 = 7.088723439

Reorder the terms:
10.5 + x = 7.088723439

Solving
10.5 + x = 7.088723439

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 7.088723439 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 7.088723439 + -10.5
x = 7.088723439 + -10.5

Combine like terms: 7.088723439 + -10.5 = -3.411276561
x = -3.411276561

Simplifying
x = -3.411276561


Subproblem 2
x + 10.5 = -7.088723439

Simplifying
x + 10.5 = -7.088723439

Reorder the terms:
10.5 + x = -7.088723439

Solving
10.5 + x = -7.088723439

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -7.088723439 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -7.088723439 + -10.5
x = -7.088723439 + -10.5

Combine like terms: -7.088723439 + -10.5 = -17.588723439
x = -17.588723439

Simplifying
x = -17.588723439


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.411276561, -17.588723439}
Solution
x = {-3.411276561, -17.588723439}

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