40=t^2-2t-7

Solution for 40=t^2-2t-7 equation:

Simplifying
40 = t2 + -2t + -7

Reorder the terms:
40 = -7 + -2t + t2

Solving
40 = -7 + -2t + t2

Solving for variable 't'.

Combine like terms: 40 + 7 = 47
47 + 2t + -1t2 = -7 + -2t + t2 + 7 + 2t + -1t2

Reorder the terms:
47 + 2t + -1t2 = -7 + 7 + -2t + 2t + t2 + -1t2

Combine like terms: -7 + 7 = 0
47 + 2t + -1t2 = 0 + -2t + 2t + t2 + -1t2
47 + 2t + -1t2 = -2t + 2t + t2 + -1t2

Combine like terms: -2t + 2t = 0
47 + 2t + -1t2 = 0 + t2 + -1t2
47 + 2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
47 + 2t + -1t2 = 0

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

Divide each side by '-1'.
-47 + -2t + t2 = 0

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -2t + 47 + t2 = 0 + 47

Reorder the terms:
-47 + 47 + -2t + t2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -2t + t2 = 0 + 47
-2t + t2 = 0 + 47

Combine like terms: 0 + 47 = 47
-2t + t2 = 47

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 47 + 1

Reorder the terms:
1 + -2t + t2 = 47 + 1

Combine like terms: 47 + 1 = 48
1 + -2t + t2 = 48

Factor a perfect square on the left side:
(t + -1)(t + -1) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(t + -1) equal to 6.92820323 and -6.92820323.

Subproblem 1
t + -1 = 6.92820323

Simplifying
t + -1 = 6.92820323

Reorder the terms:
-1 + t = 6.92820323

Solving
-1 + t = 6.92820323

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 6.92820323 + 1

Combine like terms: -1 + 1 = 0
0 + t = 6.92820323 + 1
t = 6.92820323 + 1

Combine like terms: 6.92820323 + 1 = 7.92820323
t = 7.92820323

Simplifying
t = 7.92820323

Subproblem 2
t + -1 = -6.92820323

Simplifying
t + -1 = -6.92820323

Reorder the terms:
-1 + t = -6.92820323

Solving
-1 + t = -6.92820323

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -6.92820323 + 1

Combine like terms: -1 + 1 = 0
0 + t = -6.92820323 + 1
t = -6.92820323 + 1

Combine like terms: -6.92820323 + 1 = -5.92820323
t = -5.92820323

Simplifying
t = -5.92820323

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.92820323, -5.92820323}