a^2-1100a=-58225.8

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Solution for a^2-1100a=-58225.8 equation:


Simplifying
a2 + -1100a = -58225.8

Reorder the terms:
-1100a + a2 = -58225.8

Solving
-1100a + a2 = -58225.8

Solving for variable 'a'.

Reorder the terms:
58225.8 + -1100a + a2 = -58225.8 + 58225.8

Combine like terms: -58225.8 + 58225.8 = 0.0
58225.8 + -1100a + a2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-58225.8' to each side of the equation.
58225.8 + -1100a + -58225.8 + a2 = 0.0 + -58225.8

Reorder the terms:
58225.8 + -58225.8 + -1100a + a2 = 0.0 + -58225.8

Combine like terms: 58225.8 + -58225.8 = 0.0
0.0 + -1100a + a2 = 0.0 + -58225.8
-1100a + a2 = 0.0 + -58225.8

Combine like terms: 0.0 + -58225.8 = -58225.8
-1100a + a2 = -58225.8

The a term is -1100a.  Take half its coefficient (-550).
Square it (302500) and add it to both sides.

Add '302500' to each side of the equation.
-1100a + 302500 + a2 = -58225.8 + 302500

Reorder the terms:
302500 + -1100a + a2 = -58225.8 + 302500

Combine like terms: -58225.8 + 302500 = 244274.2
302500 + -1100a + a2 = 244274.2

Factor a perfect square on the left side:
(a + -550)(a + -550) = 244274.2

Calculate the square root of the right side: 494.241034314

Break this problem into two subproblems by setting 
(a + -550) equal to 494.241034314 and -494.241034314.


Subproblem 1
a + -550 = 494.241034314

Simplifying
a + -550 = 494.241034314

Reorder the terms:
-550 + a = 494.241034314

Solving
-550 + a = 494.241034314

Solving for variable 'a'.

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

Add '550' to each side of the equation.
-550 + 550 + a = 494.241034314 + 550

Combine like terms: -550 + 550 = 0
0 + a = 494.241034314 + 550
a = 494.241034314 + 550

Combine like terms: 494.241034314 + 550 = 1044.241034314
a = 1044.241034314

Simplifying
a = 1044.241034314


Subproblem 2
a + -550 = -494.241034314

Simplifying
a + -550 = -494.241034314

Reorder the terms:
-550 + a = -494.241034314

Solving
-550 + a = -494.241034314

Solving for variable 'a'.

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

Add '550' to each side of the equation.
-550 + 550 + a = -494.241034314 + 550

Combine like terms: -550 + 550 = 0
0 + a = -494.241034314 + 550
a = -494.241034314 + 550

Combine like terms: -494.241034314 + 550 = 55.758965686
a = 55.758965686

Simplifying
a = 55.758965686


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1044.241034314, 55.758965686}

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