64(t)=64-t^2

Solution for 64(t)=64-t^2 equation:

Simplifying
64(t) = 64 + -1t2

Solving
64t = 64 + -1t2

Solving for variable 't'.

Reorder the terms:
-64 + 64t + t2 = 64 + -1t2 + -64 + t2

Reorder the terms:
-64 + 64t + t2 = 64 + -64 + -1t2 + t2

Combine like terms: 64 + -64 = 0
-64 + 64t + t2 = 0 + -1t2 + t2
-64 + 64t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-64 + 64t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 64t + 64 + t2 = 0 + 64

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

Combine like terms: -64 + 64 = 0
0 + 64t + t2 = 0 + 64
64t + t2 = 0 + 64

Combine like terms: 0 + 64 = 64
64t + t2 = 64

The t term is 64t.  Take half its coefficient (32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
64t + 1024 + t2 = 64 + 1024

Reorder the terms:
1024 + 64t + t2 = 64 + 1024

Combine like terms: 64 + 1024 = 1088
1024 + 64t + t2 = 1088

Factor a perfect square on the left side:
(t + 32)(t + 32) = 1088

Calculate the square root of the right side: 32.984845005

Break this problem into two subproblems by setting 
(t + 32) equal to 32.984845005 and -32.984845005.

Subproblem 1
t + 32 = 32.984845005

Simplifying
t + 32 = 32.984845005

Reorder the terms:
32 + t = 32.984845005

Solving
32 + t = 32.984845005

Solving for variable 't'.

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

Add '-32' to each side of the equation.
32 + -32 + t = 32.984845005 + -32

Combine like terms: 32 + -32 = 0
0 + t = 32.984845005 + -32
t = 32.984845005 + -32

Combine like terms: 32.984845005 + -32 = 0.984845005
t = 0.984845005

Simplifying
t = 0.984845005

Subproblem 2
t + 32 = -32.984845005

Simplifying
t + 32 = -32.984845005

Reorder the terms:
32 + t = -32.984845005

Solving
32 + t = -32.984845005

Solving for variable 't'.

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

Add '-32' to each side of the equation.
32 + -32 + t = -32.984845005 + -32

Combine like terms: 32 + -32 = 0
0 + t = -32.984845005 + -32
t = -32.984845005 + -32

Combine like terms: -32.984845005 + -32 = -64.984845005
t = -64.984845005

Simplifying
t = -64.984845005

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.984845005, -64.984845005}