t*t+2t-48=11

Solution for t*t+2t-48=11 equation:

Simplifying
t * t + 2t + -48 = 11

Multiply t * t
t2 + 2t + -48 = 11

Reorder the terms:
-48 + 2t + t2 = 11

Solving
-48 + 2t + t2 = 11

Solving for variable 't'.

Reorder the terms:
-48 + -11 + 2t + t2 = 11 + -11

Combine like terms: -48 + -11 = -59
-59 + 2t + t2 = 11 + -11

Combine like terms: 11 + -11 = 0
-59 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 2t + 59 + t2 = 0 + 59

Reorder the terms:
-59 + 59 + 2t + t2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 2t + t2 = 0 + 59
2t + t2 = 0 + 59

Combine like terms: 0 + 59 = 59
2t + t2 = 59

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 = 59 + 1

Reorder the terms:
1 + 2t + t2 = 59 + 1

Combine like terms: 59 + 1 = 60
1 + 2t + t2 = 60

Factor a perfect square on the left side:
(t + 1)(t + 1) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(t + 1) equal to 7.745966692 and -7.745966692.

Subproblem 1
t + 1 = 7.745966692

Simplifying
t + 1 = 7.745966692

Reorder the terms:
1 + t = 7.745966692

Solving
1 + t = 7.745966692

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 = 7.745966692 + -1

Combine like terms: 1 + -1 = 0
0 + t = 7.745966692 + -1
t = 7.745966692 + -1

Combine like terms: 7.745966692 + -1 = 6.745966692
t = 6.745966692

Simplifying
t = 6.745966692

Subproblem 2
t + 1 = -7.745966692

Simplifying
t + 1 = -7.745966692

Reorder the terms:
1 + t = -7.745966692

Solving
1 + t = -7.745966692

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 = -7.745966692 + -1

Combine like terms: 1 + -1 = 0
0 + t = -7.745966692 + -1
t = -7.745966692 + -1

Combine like terms: -7.745966692 + -1 = -8.745966692
t = -8.745966692

Simplifying
t = -8.745966692

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.745966692, -8.745966692}