a^2-900a-22500=0

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Solution for a^2-900a-22500=0 equation: 


Simplifying
a2 + -900a + -22500 = 0

Reorder the terms:
-22500 + -900a + a2 = 0

Solving
-22500 + -900a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '22500' to each side of the equation.
-22500 + -900a + 22500 + a2 = 0 + 22500

Reorder the terms:
-22500 + 22500 + -900a + a2 = 0 + 22500

Combine like terms: -22500 + 22500 = 0
0 + -900a + a2 = 0 + 22500
-900a + a2 = 0 + 22500

Combine like terms: 0 + 22500 = 22500
-900a + a2 = 22500

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 = 22500 + 202500

Reorder the terms:
202500 + -900a + a2 = 22500 + 202500

Combine like terms: 22500 + 202500 = 225000
202500 + -900a + a2 = 225000

Factor a perfect square on the left side:
(a + -450)(a + -450) = 225000

Calculate the square root of the right side: 474.341649025

Break this problem into two subproblems by setting 
(a + -450) equal to 474.341649025 and -474.341649025.


Subproblem 1
a + -450 = 474.341649025

Simplifying
a + -450 = 474.341649025

Reorder the terms:
-450 + a = 474.341649025

Solving
-450 + a = 474.341649025

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 = 474.341649025 + 450

Combine like terms: -450 + 450 = 0
0 + a = 474.341649025 + 450
a = 474.341649025 + 450

Combine like terms: 474.341649025 + 450 = 924.341649025
a = 924.341649025

Simplifying
a = 924.341649025


Subproblem 2
a + -450 = -474.341649025

Simplifying
a + -450 = -474.341649025

Reorder the terms:
-450 + a = -474.341649025

Solving
-450 + a = -474.341649025

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 = -474.341649025 + 450

Combine like terms: -450 + 450 = 0
0 + a = -474.341649025 + 450
a = -474.341649025 + 450

Combine like terms: -474.341649025 + 450 = -24.341649025
a = -24.341649025

Simplifying
a = -24.341649025


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {924.341649025, -24.341649025}

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