t*t+2t-48=13

Solution for t*t+2t-48=13 equation:

Simplifying
t * t + 2t + -48 = 13

Multiply t * t
t2 + 2t + -48 = 13

Reorder the terms:
-48 + 2t + t2 = 13

Solving
-48 + 2t + t2 = 13

Solving for variable 't'.

Reorder the terms:
-48 + -13 + 2t + t2 = 13 + -13

Combine like terms: -48 + -13 = -61
-61 + 2t + t2 = 13 + -13

Combine like terms: 13 + -13 = 0
-61 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + 2t + 61 + t2 = 0 + 61

Reorder the terms:
-61 + 61 + 2t + t2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 2t + t2 = 0 + 61
2t + t2 = 0 + 61

Combine like terms: 0 + 61 = 61
2t + t2 = 61

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 = 61 + 1

Reorder the terms:
1 + 2t + t2 = 61 + 1

Combine like terms: 61 + 1 = 62
1 + 2t + t2 = 62

Factor a perfect square on the left side:
(t + 1)(t + 1) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(t + 1) equal to 7.874007874 and -7.874007874.

Subproblem 1
t + 1 = 7.874007874

Simplifying
t + 1 = 7.874007874

Reorder the terms:
1 + t = 7.874007874

Solving
1 + t = 7.874007874

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 = 7.874007874 + -1

Combine like terms: 1 + -1 = 0
0 + t = 7.874007874 + -1
t = 7.874007874 + -1

Combine like terms: 7.874007874 + -1 = 6.874007874
t = 6.874007874

Simplifying
t = 6.874007874

Subproblem 2
t + 1 = -7.874007874

Simplifying
t + 1 = -7.874007874

Reorder the terms:
1 + t = -7.874007874

Solving
1 + t = -7.874007874

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 = -7.874007874 + -1

Combine like terms: 1 + -1 = 0
0 + t = -7.874007874 + -1
t = -7.874007874 + -1

Combine like terms: -7.874007874 + -1 = -8.874007874
t = -8.874007874

Simplifying
t = -8.874007874

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.874007874, -8.874007874}