t^2+2=6t

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


Simplifying
t2 + 2 = 6t

Reorder the terms:
2 + t2 = 6t

Solving
2 + t2 = 6t

Solving for variable 't'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -6t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -6t + t2 = 0 + -2

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

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

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -2 + 9

Reorder the terms:
9 + -6t + t2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6t + t2 = 7

Factor a perfect square on the left side:
(t + -3)(t + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1

t + -3 = 2.645751311 Simplifying t + -3 = 2.645751311 Reorder the terms: -3 + t = 2.645751311 Solving -3 + t = 2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.645751311 + 3 t = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 t = 5.645751311 Simplifying t = 5.645751311

Subproblem 2

t + -3 = -2.645751311 Simplifying t + -3 = -2.645751311 Reorder the terms: -3 + t = -2.645751311 Solving -3 + t = -2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.645751311 + 3 t = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 t = 0.354248689 Simplifying t = 0.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.645751311, 0.354248689}

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