2t^2-64t+32=0

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Solution for 2t^2-64t+32=0 equation: 


Simplifying
2t2 + -64t + 32 = 0

Reorder the terms:
32 + -64t + 2t2 = 0

Solving
32 + -64t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -32t + t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -32t + t2)' equal to zero and attempt to solve:

Simplifying
16 + -32t + t2 = 0

Solving
16 + -32t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -32t + -16 + t2 = 0 + -16

Reorder the terms:
16 + -16 + -32t + t2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -32t + t2 = 0 + -16
-32t + t2 = 0 + -16

Combine like terms: 0 + -16 = -16
-32t + t2 = -16

The t term is -32t.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32t + 256 + t2 = -16 + 256

Reorder the terms:
256 + -32t + t2 = -16 + 256

Combine like terms: -16 + 256 = 240
256 + -32t + t2 = 240

Factor a perfect square on the left side:
(t + -16)(t + -16) = 240

Calculate the square root of the right side: 15.491933385

Break this problem into two subproblems by setting 
(t + -16) equal to 15.491933385 and -15.491933385.


Subproblem 1
t + -16 = 15.491933385

Simplifying
t + -16 = 15.491933385

Reorder the terms:
-16 + t = 15.491933385

Solving
-16 + t = 15.491933385

Solving for variable 't'.

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

Add '16' to each side of the equation.
-16 + 16 + t = 15.491933385 + 16

Combine like terms: -16 + 16 = 0
0 + t = 15.491933385 + 16
t = 15.491933385 + 16

Combine like terms: 15.491933385 + 16 = 31.491933385
t = 31.491933385

Simplifying
t = 31.491933385


Subproblem 2
t + -16 = -15.491933385

Simplifying
t + -16 = -15.491933385

Reorder the terms:
-16 + t = -15.491933385

Solving
-16 + t = -15.491933385

Solving for variable 't'.

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

Add '16' to each side of the equation.
-16 + 16 + t = -15.491933385 + 16

Combine like terms: -16 + 16 = 0
0 + t = -15.491933385 + 16
t = -15.491933385 + 16

Combine like terms: -15.491933385 + 16 = 0.508066615
t = 0.508066615

Simplifying
t = 0.508066615


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {31.491933385, 0.508066615}
Solution
t = {31.491933385, 0.508066615}

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