4t^2+64t-32=0

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Solution for 4t^2+64t-32=0 equation: 


Simplifying
4t2 + 64t + -32 = 0

Reorder the terms:
-32 + 64t + 4t2 = 0

Solving
-32 + 64t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 16t + t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-8 + 16t + t2)' equal to zero and attempt to solve:

Simplifying
-8 + 16t + t2 = 0

Solving
-8 + 16t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 16t + 8 + t2 = 0 + 8

Reorder the terms:
-8 + 8 + 16t + t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 16t + t2 = 0 + 8
16t + t2 = 0 + 8

Combine like terms: 0 + 8 = 8
16t + t2 = 8

The t term is 16t.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16t + 64 + t2 = 8 + 64

Reorder the terms:
64 + 16t + t2 = 8 + 64

Combine like terms: 8 + 64 = 72
64 + 16t + t2 = 72

Factor a perfect square on the left side:
(t + 8)(t + 8) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(t + 8) equal to 8.485281374 and -8.485281374.


Subproblem 1
t + 8 = 8.485281374

Simplifying
t + 8 = 8.485281374

Reorder the terms:
8 + t = 8.485281374

Solving
8 + t = 8.485281374

Solving for variable 't'.

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

Add '-8' to each side of the equation.
8 + -8 + t = 8.485281374 + -8

Combine like terms: 8 + -8 = 0
0 + t = 8.485281374 + -8
t = 8.485281374 + -8

Combine like terms: 8.485281374 + -8 = 0.485281374
t = 0.485281374

Simplifying
t = 0.485281374


Subproblem 2
t + 8 = -8.485281374

Simplifying
t + 8 = -8.485281374

Reorder the terms:
8 + t = -8.485281374

Solving
8 + t = -8.485281374

Solving for variable 't'.

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

Add '-8' to each side of the equation.
8 + -8 + t = -8.485281374 + -8

Combine like terms: 8 + -8 = 0
0 + t = -8.485281374 + -8
t = -8.485281374 + -8

Combine like terms: -8.485281374 + -8 = -16.485281374
t = -16.485281374

Simplifying
t = -16.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.485281374, -16.485281374}
Solution
t = {0.485281374, -16.485281374}

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