a^2-1100a=-57939.16

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Solution for a^2-1100a=-57939.16 equation:


Simplifying
a2 + -1100a = -57939.16

Reorder the terms:
-1100a + a2 = -57939.16

Solving
-1100a + a2 = -57939.16

Solving for variable 'a'.

Reorder the terms:
57939.16 + -1100a + a2 = -57939.16 + 57939.16

Combine like terms: -57939.16 + 57939.16 = 0.00
57939.16 + -1100a + a2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-57939.16' to each side of the equation.
57939.16 + -1100a + -57939.16 + a2 = 0.00 + -57939.16

Reorder the terms:
57939.16 + -57939.16 + -1100a + a2 = 0.00 + -57939.16

Combine like terms: 57939.16 + -57939.16 = 0.00
0.00 + -1100a + a2 = 0.00 + -57939.16
-1100a + a2 = 0.00 + -57939.16

Combine like terms: 0.00 + -57939.16 = -57939.16
-1100a + a2 = -57939.16

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 = -57939.16 + 302500

Reorder the terms:
302500 + -1100a + a2 = -57939.16 + 302500

Combine like terms: -57939.16 + 302500 = 244560.84
302500 + -1100a + a2 = 244560.84

Factor a perfect square on the left side:
(a + -550)(a + -550) = 244560.84

Calculate the square root of the right side: 494.530929265

Break this problem into two subproblems by setting 
(a + -550) equal to 494.530929265 and -494.530929265.


Subproblem 1
a + -550 = 494.530929265

Simplifying
a + -550 = 494.530929265

Reorder the terms:
-550 + a = 494.530929265

Solving
-550 + a = 494.530929265

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 = 494.530929265 + 550

Combine like terms: -550 + 550 = 0
0 + a = 494.530929265 + 550
a = 494.530929265 + 550

Combine like terms: 494.530929265 + 550 = 1044.530929265
a = 1044.530929265

Simplifying
a = 1044.530929265


Subproblem 2
a + -550 = -494.530929265

Simplifying
a + -550 = -494.530929265

Reorder the terms:
-550 + a = -494.530929265

Solving
-550 + a = -494.530929265

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 = -494.530929265 + 550

Combine like terms: -550 + 550 = 0
0 + a = -494.530929265 + 550
a = -494.530929265 + 550

Combine like terms: -494.530929265 + 550 = 55.469070735
a = 55.469070735

Simplifying
a = 55.469070735


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1044.530929265, 55.469070735}

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