t^2+2t+2=6

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Solution for t^2+2t+2=6 equation:


Simplifying
t2 + 2t + 2 = 6

Reorder the terms:
2 + 2t + t2 = 6

Solving
2 + 2t + t2 = 6

Solving for variable 't'.

Reorder the terms:
2 + -6 + 2t + t2 = 6 + -6

Combine like terms: 2 + -6 = -4
-4 + 2t + t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-4 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + 2t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2t + t2 = 0 + 4
2t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
2t + t2 = 4

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 = 4 + 1

Reorder the terms:
1 + 2t + t2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + 2t + t2 = 5

Factor a perfect square on the left side:
(t + 1)(t + 1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(t + 1) equal to 2.236067978 and -2.236067978.

Subproblem 1

t + 1 = 2.236067978 Simplifying t + 1 = 2.236067978 Reorder the terms: 1 + t = 2.236067978 Solving 1 + t = 2.236067978 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 = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + t = 2.236067978 + -1 t = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 t = 1.236067978 Simplifying t = 1.236067978

Subproblem 2

t + 1 = -2.236067978 Simplifying t + 1 = -2.236067978 Reorder the terms: 1 + t = -2.236067978 Solving 1 + t = -2.236067978 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 = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + t = -2.236067978 + -1 t = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 t = -3.236067978 Simplifying t = -3.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.236067978, -3.236067978}

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