a^2-900a+54465.22=0

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Solution for a^2-900a+54465.22=0 equation:


Simplifying
a2 + -900a + 54465.22 = 0

Reorder the terms:
54465.22 + -900a + a2 = 0

Solving
54465.22 + -900a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-54465.22' to each side of the equation.
54465.22 + -900a + -54465.22 + a2 = 0 + -54465.22

Reorder the terms:
54465.22 + -54465.22 + -900a + a2 = 0 + -54465.22

Combine like terms: 54465.22 + -54465.22 = 0.00
0.00 + -900a + a2 = 0 + -54465.22
-900a + a2 = 0 + -54465.22

Combine like terms: 0 + -54465.22 = -54465.22
-900a + a2 = -54465.22

The a term is -900a.  Take half its coefficient (-450).
Square it (202500) and add it to both sides.

Add '202500' to each side of the equation.
-900a + 202500 + a2 = -54465.22 + 202500

Reorder the terms:
202500 + -900a + a2 = -54465.22 + 202500

Combine like terms: -54465.22 + 202500 = 148034.78
202500 + -900a + a2 = 148034.78

Factor a perfect square on the left side:
(a + -450)(a + -450) = 148034.78

Calculate the square root of the right side: 384.752881731

Break this problem into two subproblems by setting 
(a + -450) equal to 384.752881731 and -384.752881731.


Subproblem 1
a + -450 = 384.752881731

Simplifying
a + -450 = 384.752881731

Reorder the terms:
-450 + a = 384.752881731

Solving
-450 + a = 384.752881731

Solving for variable 'a'.

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

Add '450' to each side of the equation.
-450 + 450 + a = 384.752881731 + 450

Combine like terms: -450 + 450 = 0
0 + a = 384.752881731 + 450
a = 384.752881731 + 450

Combine like terms: 384.752881731 + 450 = 834.752881731
a = 834.752881731

Simplifying
a = 834.752881731


Subproblem 2
a + -450 = -384.752881731

Simplifying
a + -450 = -384.752881731

Reorder the terms:
-450 + a = -384.752881731

Solving
-450 + a = -384.752881731

Solving for variable 'a'.

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

Add '450' to each side of the equation.
-450 + 450 + a = -384.752881731 + 450

Combine like terms: -450 + 450 = 0
0 + a = -384.752881731 + 450
a = -384.752881731 + 450

Combine like terms: -384.752881731 + 450 = 65.247118269
a = 65.247118269

Simplifying
a = 65.247118269


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {834.752881731, 65.247118269}

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