a^2-10a-2100=0

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Solution for a^2-10a-2100=0 equation: 


Simplifying
a2 + -10a + -2100 = 0

Reorder the terms:
-2100 + -10a + a2 = 0

Solving
-2100 + -10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '2100' to each side of the equation.
-2100 + -10a + 2100 + a2 = 0 + 2100

Reorder the terms:
-2100 + 2100 + -10a + a2 = 0 + 2100

Combine like terms: -2100 + 2100 = 0
0 + -10a + a2 = 0 + 2100
-10a + a2 = 0 + 2100

Combine like terms: 0 + 2100 = 2100
-10a + a2 = 2100

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = 2100 + 25

Reorder the terms:
25 + -10a + a2 = 2100 + 25

Combine like terms: 2100 + 25 = 2125
25 + -10a + a2 = 2125

Factor a perfect square on the left side:
(a + -5)(a + -5) = 2125

Calculate the square root of the right side: 46.097722286

Break this problem into two subproblems by setting 
(a + -5) equal to 46.097722286 and -46.097722286.


Subproblem 1
a + -5 = 46.097722286

Simplifying
a + -5 = 46.097722286

Reorder the terms:
-5 + a = 46.097722286

Solving
-5 + a = 46.097722286

Solving for variable 'a'.

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

Add '5' to each side of the equation.
-5 + 5 + a = 46.097722286 + 5

Combine like terms: -5 + 5 = 0
0 + a = 46.097722286 + 5
a = 46.097722286 + 5

Combine like terms: 46.097722286 + 5 = 51.097722286
a = 51.097722286

Simplifying
a = 51.097722286


Subproblem 2
a + -5 = -46.097722286

Simplifying
a + -5 = -46.097722286

Reorder the terms:
-5 + a = -46.097722286

Solving
-5 + a = -46.097722286

Solving for variable 'a'.

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

Add '5' to each side of the equation.
-5 + 5 + a = -46.097722286 + 5

Combine like terms: -5 + 5 = 0
0 + a = -46.097722286 + 5
a = -46.097722286 + 5

Combine like terms: -46.097722286 + 5 = -41.097722286
a = -41.097722286

Simplifying
a = -41.097722286


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {51.097722286, -41.097722286}

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