2a^2-3616a+32=0

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Solution for 2a^2-3616a+32=0 equation: 


Simplifying
2a2 + -3616a + 32 = 0

Reorder the terms:
32 + -3616a + 2a2 = 0

Solving
32 + -3616a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -1808a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -1808a + a2)' equal to zero and attempt to solve:

Simplifying
16 + -1808a + a2 = 0

Solving
16 + -1808a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -1808a + -16 + a2 = 0 + -16

Reorder the terms:
16 + -16 + -1808a + a2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1808a + a2 = 0 + -16
-1808a + a2 = 0 + -16

Combine like terms: 0 + -16 = -16
-1808a + a2 = -16

The a term is -1808a.  Take half its coefficient (-904).
Square it (817216) and add it to both sides.

Add '817216' to each side of the equation.
-1808a + 817216 + a2 = -16 + 817216

Reorder the terms:
817216 + -1808a + a2 = -16 + 817216

Combine like terms: -16 + 817216 = 817200
817216 + -1808a + a2 = 817200

Factor a perfect square on the left side:
(a + -904)(a + -904) = 817200

Calculate the square root of the right side: 903.991150399

Break this problem into two subproblems by setting 
(a + -904) equal to 903.991150399 and -903.991150399.


Subproblem 1
a + -904 = 903.991150399

Simplifying
a + -904 = 903.991150399

Reorder the terms:
-904 + a = 903.991150399

Solving
-904 + a = 903.991150399

Solving for variable 'a'.

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

Add '904' to each side of the equation.
-904 + 904 + a = 903.991150399 + 904

Combine like terms: -904 + 904 = 0
0 + a = 903.991150399 + 904
a = 903.991150399 + 904

Combine like terms: 903.991150399 + 904 = 1807.991150399
a = 1807.991150399

Simplifying
a = 1807.991150399


Subproblem 2
a + -904 = -903.991150399

Simplifying
a + -904 = -903.991150399

Reorder the terms:
-904 + a = -903.991150399

Solving
-904 + a = -903.991150399

Solving for variable 'a'.

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

Add '904' to each side of the equation.
-904 + 904 + a = -903.991150399 + 904

Combine like terms: -904 + 904 = 0
0 + a = -903.991150399 + 904
a = -903.991150399 + 904

Combine like terms: -903.991150399 + 904 = 0.008849601
a = 0.008849601

Simplifying
a = 0.008849601


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1807.991150399, 0.008849601}
Solution
a = {1807.991150399, 0.008849601}

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