(t+4)(t+4)=54

Solution for (t+4)(t+4)=54 equation:

Simplifying
(t + 4)(t + 4) = 54

Reorder the terms:
(4 + t)(t + 4) = 54

Reorder the terms:
(4 + t)(4 + t) = 54

Multiply (4 + t) * (4 + t)
(4(4 + t) + t(4 + t)) = 54
((4 * 4 + t * 4) + t(4 + t)) = 54
((16 + 4t) + t(4 + t)) = 54
(16 + 4t + (4 * t + t * t)) = 54
(16 + 4t + (4t + t2)) = 54

Combine like terms: 4t + 4t = 8t
(16 + 8t + t2) = 54

Solving
16 + 8t + t2 = 54

Solving for variable 't'.

Reorder the terms:
16 + -54 + 8t + t2 = 54 + -54

Combine like terms: 16 + -54 = -38
-38 + 8t + t2 = 54 + -54

Combine like terms: 54 + -54 = 0
-38 + 8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 8t + 38 + t2 = 0 + 38

Reorder the terms:
-38 + 38 + 8t + t2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 8t + t2 = 0 + 38
8t + t2 = 0 + 38

Combine like terms: 0 + 38 = 38
8t + t2 = 38

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = 38 + 16

Reorder the terms:
16 + 8t + t2 = 38 + 16

Combine like terms: 38 + 16 = 54
16 + 8t + t2 = 54

Factor a perfect square on the left side:
(t + 4)(t + 4) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(t + 4) equal to 7.348469228 and -7.348469228.

Subproblem 1
t + 4 = 7.348469228

Simplifying
t + 4 = 7.348469228

Reorder the terms:
4 + t = 7.348469228

Solving
4 + t = 7.348469228

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = 7.348469228 + -4

Combine like terms: 4 + -4 = 0
0 + t = 7.348469228 + -4
t = 7.348469228 + -4

Combine like terms: 7.348469228 + -4 = 3.348469228
t = 3.348469228

Simplifying
t = 3.348469228

Subproblem 2
t + 4 = -7.348469228

Simplifying
t + 4 = -7.348469228

Reorder the terms:
4 + t = -7.348469228

Solving
4 + t = -7.348469228

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = -7.348469228 + -4

Combine like terms: 4 + -4 = 0
0 + t = -7.348469228 + -4
t = -7.348469228 + -4

Combine like terms: -7.348469228 + -4 = -11.348469228
t = -11.348469228

Simplifying
t = -11.348469228

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.348469228, -11.348469228}