56=t^2-t-56

Solution for 56=t^2-t-56 equation:

Simplifying
56 = t2 + -1t + -56

Reorder the terms:
56 = -56 + -1t + t2

Solving
56 = -56 + -1t + t2

Solving for variable 't'.

Combine like terms: 56 + 56 = 112
112 + t + -1t2 = -56 + -1t + t2 + 56 + t + -1t2

Reorder the terms:
112 + t + -1t2 = -56 + 56 + -1t + t + t2 + -1t2

Combine like terms: -56 + 56 = 0
112 + t + -1t2 = 0 + -1t + t + t2 + -1t2
112 + t + -1t2 = -1t + t + t2 + -1t2

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-112 + -1t + t2 = 0

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + -1t + 112 + t2 = 0 + 112

Reorder the terms:
-112 + 112 + -1t + t2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + -1t + t2 = 0 + 112
-1t + t2 = 0 + 112

Combine like terms: 0 + 112 = 112
-1t + t2 = 112

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

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 112 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 112 + 0.25

Combine like terms: 112 + 0.25 = 112.25
0.25 + -1t + t2 = 112.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(t + 0.5) equal to 10.59481005 and -10.59481005.

Subproblem 1
t + 0.5 = 10.59481005

Simplifying
t + 0.5 = 10.59481005

Reorder the terms:
0.5 + t = 10.59481005

Solving
0.5 + t = 10.59481005

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 10.59481005 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 10.59481005 + -0.5
t = 10.59481005 + -0.5

Combine like terms: 10.59481005 + -0.5 = 10.09481005
t = 10.09481005

Simplifying
t = 10.09481005

Subproblem 2
t + 0.5 = -10.59481005

Simplifying
t + 0.5 = -10.59481005

Reorder the terms:
0.5 + t = -10.59481005

Solving
0.5 + t = -10.59481005

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -10.59481005 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -10.59481005 + -0.5
t = -10.59481005 + -0.5

Combine like terms: -10.59481005 + -0.5 = -11.09481005
t = -11.09481005

Simplifying
t = -11.09481005

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.09481005, -11.09481005}