t^2+7t-1=0

Solution for t^2+7t-1=0 equation:

Simplifying
t2 + 7t + -1 = 0

Reorder the terms:
-1 + 7t + t2 = 0

Solving
-1 + 7t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 7t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + 7t + t2 = 0 + 1

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

Combine like terms: 0 + 1 = 1
7t + t2 = 1

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 = 1 + 12.25

Reorder the terms:
12.25 + 7t + t2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + 7t + t2 = 13.25

Factor a perfect square on the left side:
(t + 3.5)(t + 3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(t + 3.5) equal to 3.640054945 and -3.640054945.

Subproblem 1
t + 3.5 = 3.640054945

Simplifying
t + 3.5 = 3.640054945

Reorder the terms:
3.5 + t = 3.640054945

Solving
3.5 + t = 3.640054945

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 = 3.640054945 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = 3.640054945 + -3.5
t = 3.640054945 + -3.5

Combine like terms: 3.640054945 + -3.5 = 0.140054945
t = 0.140054945

Simplifying
t = 0.140054945

Subproblem 2
t + 3.5 = -3.640054945

Simplifying
t + 3.5 = -3.640054945

Reorder the terms:
3.5 + t = -3.640054945

Solving
3.5 + t = -3.640054945

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 = -3.640054945 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = -3.640054945 + -3.5
t = -3.640054945 + -3.5

Combine like terms: -3.640054945 + -3.5 = -7.140054945
t = -7.140054945

Simplifying
t = -7.140054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.140054945, -7.140054945}