t^2-3t-7=0

Solution for t^2-3t-7=0 equation:

Simplifying
t2 + -3t + -7 = 0

Reorder the terms:
-7 + -3t + t2 = 0

Solving
-7 + -3t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + -3t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3t + t2 = 0 + 7
-3t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3t + t2 = 7

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 7 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + -3t + t2 = 9.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(t + -1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
t + -1.5 = 3.041381265

Simplifying
t + -1.5 = 3.041381265

Reorder the terms:
-1.5 + t = 3.041381265

Solving
-1.5 + t = 3.041381265

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 3.041381265 + 1.5
t = 3.041381265 + 1.5

Combine like terms: 3.041381265 + 1.5 = 4.541381265
t = 4.541381265

Simplifying
t = 4.541381265

Subproblem 2
t + -1.5 = -3.041381265

Simplifying
t + -1.5 = -3.041381265

Reorder the terms:
-1.5 + t = -3.041381265

Solving
-1.5 + t = -3.041381265

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -3.041381265 + 1.5
t = -3.041381265 + 1.5

Combine like terms: -3.041381265 + 1.5 = -1.541381265
t = -1.541381265

Simplifying
t = -1.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.541381265, -1.541381265}