a^2-200a+4233.6=0

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Solution for a^2-200a+4233.6=0 equation:


Simplifying
a2 + -200a + 4233.6 = 0

Reorder the terms:
4233.6 + -200a + a2 = 0

Solving
4233.6 + -200a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-4233.6' to each side of the equation.
4233.6 + -200a + -4233.6 + a2 = 0 + -4233.6

Reorder the terms:
4233.6 + -4233.6 + -200a + a2 = 0 + -4233.6

Combine like terms: 4233.6 + -4233.6 = 0.0
0.0 + -200a + a2 = 0 + -4233.6
-200a + a2 = 0 + -4233.6

Combine like terms: 0 + -4233.6 = -4233.6
-200a + a2 = -4233.6

The a term is -200a.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200a + 10000 + a2 = -4233.6 + 10000

Reorder the terms:
10000 + -200a + a2 = -4233.6 + 10000

Combine like terms: -4233.6 + 10000 = 5766.4
10000 + -200a + a2 = 5766.4

Factor a perfect square on the left side:
(a + -100)(a + -100) = 5766.4

Calculate the square root of the right side: 75.936815841

Break this problem into two subproblems by setting 
(a + -100) equal to 75.936815841 and -75.936815841.

Subproblem 1

a + -100 = 75.936815841 Simplifying a + -100 = 75.936815841 Reorder the terms: -100 + a = 75.936815841 Solving -100 + a = 75.936815841 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + a = 75.936815841 + 100 Combine like terms: -100 + 100 = 0 0 + a = 75.936815841 + 100 a = 75.936815841 + 100 Combine like terms: 75.936815841 + 100 = 175.936815841 a = 175.936815841 Simplifying a = 175.936815841

Subproblem 2

a + -100 = -75.936815841 Simplifying a + -100 = -75.936815841 Reorder the terms: -100 + a = -75.936815841 Solving -100 + a = -75.936815841 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + a = -75.936815841 + 100 Combine like terms: -100 + 100 = 0 0 + a = -75.936815841 + 100 a = -75.936815841 + 100 Combine like terms: -75.936815841 + 100 = 24.063184159 a = 24.063184159 Simplifying a = 24.063184159

Solution

The solution to the problem is based on the solutions from the subproblems. a = {175.936815841, 24.063184159}

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