32t+64(t)(t)=88

Solution for 32t+64(t)(t)=88 equation:

Simplifying
32t + 64(t)(t) = 88

Multiply t * t
32t + 64t2 = 88

Solving
32t + 64t2 = 88

Solving for variable 't'.

Reorder the terms:
-88 + 32t + 64t2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + 32t + 64t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-11 + 4t + 8t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-11 + 4t + 8t2)' equal to zero and attempt to solve:

Simplifying
-11 + 4t + 8t2 = 0

Solving
-11 + 4t + 8t2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-1.375 + 0.5t + t2 = 0

Move the constant term to the right:

Add '1.375' to each side of the equation.
-1.375 + 0.5t + 1.375 + t2 = 0 + 1.375

Reorder the terms:
-1.375 + 1.375 + 0.5t + t2 = 0 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + 0.5t + t2 = 0 + 1.375
0.5t + t2 = 0 + 1.375

Combine like terms: 0 + 1.375 = 1.375
0.5t + t2 = 1.375

The t term is 0.5t.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5t + 0.0625 + t2 = 1.375 + 0.0625

Reorder the terms:
0.0625 + 0.5t + t2 = 1.375 + 0.0625

Combine like terms: 1.375 + 0.0625 = 1.4375
0.0625 + 0.5t + t2 = 1.4375

Factor a perfect square on the left side:
(t + 0.25)(t + 0.25) = 1.4375

Calculate the square root of the right side: 1.198957881

Break this problem into two subproblems by setting 
(t + 0.25) equal to 1.198957881 and -1.198957881.

Subproblem 1
t + 0.25 = 1.198957881

Simplifying
t + 0.25 = 1.198957881

Reorder the terms:
0.25 + t = 1.198957881

Solving
0.25 + t = 1.198957881

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = 1.198957881 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = 1.198957881 + -0.25
t = 1.198957881 + -0.25

Combine like terms: 1.198957881 + -0.25 = 0.948957881
t = 0.948957881

Simplifying
t = 0.948957881

Subproblem 2
t + 0.25 = -1.198957881

Simplifying
t + 0.25 = -1.198957881

Reorder the terms:
0.25 + t = -1.198957881

Solving
0.25 + t = -1.198957881

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = -1.198957881 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = -1.198957881 + -0.25
t = -1.198957881 + -0.25

Combine like terms: -1.198957881 + -0.25 = -1.448957881
t = -1.448957881

Simplifying
t = -1.448957881

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.948957881, -1.448957881}
Solution
t = {0.948957881, -1.448957881}