t^2+7t-10.72=0

Solution for t^2+7t-10.72=0 equation:

Simplifying
t2 + 7t + -10.72 = 0

Reorder the terms:
-10.72 + 7t + t2 = 0

Solving
-10.72 + 7t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '10.72' to each side of the equation.
-10.72 + 7t + 10.72 + t2 = 0 + 10.72

Reorder the terms:
-10.72 + 10.72 + 7t + t2 = 0 + 10.72

Combine like terms: -10.72 + 10.72 = 0.00
0.00 + 7t + t2 = 0 + 10.72
7t + t2 = 0 + 10.72

Combine like terms: 0 + 10.72 = 10.72
7t + t2 = 10.72

The t term is 7t.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7t + 12.25 + t2 = 10.72 + 12.25

Reorder the terms:
12.25 + 7t + t2 = 10.72 + 12.25

Combine like terms: 10.72 + 12.25 = 22.97
12.25 + 7t + t2 = 22.97

Factor a perfect square on the left side:
(t + 3.5)(t + 3.5) = 22.97

Calculate the square root of the right side: 4.792702787

Break this problem into two subproblems by setting 
(t + 3.5) equal to 4.792702787 and -4.792702787.

Subproblem 1
t + 3.5 = 4.792702787

Simplifying
t + 3.5 = 4.792702787

Reorder the terms:
3.5 + t = 4.792702787

Solving
3.5 + t = 4.792702787

Solving for variable 't'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + t = 4.792702787 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = 4.792702787 + -3.5
t = 4.792702787 + -3.5

Combine like terms: 4.792702787 + -3.5 = 1.292702787
t = 1.292702787

Simplifying
t = 1.292702787

Subproblem 2
t + 3.5 = -4.792702787

Simplifying
t + 3.5 = -4.792702787

Reorder the terms:
3.5 + t = -4.792702787

Solving
3.5 + t = -4.792702787

Solving for variable 't'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + t = -4.792702787 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = -4.792702787 + -3.5
t = -4.792702787 + -3.5

Combine like terms: -4.792702787 + -3.5 = -8.292702787
t = -8.292702787

Simplifying
t = -8.292702787

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.292702787, -8.292702787}