3t^2-12t+2=0

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Solution for 3t^2-12t+2=0 equation:


Simplifying
3t2 + -12t + 2 = 0

Reorder the terms:
2 + -12t + 3t2 = 0

Solving
2 + -12t + 3t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.6666666667 + -4t + t2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -4t + -0.6666666667 + t2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -4t + t2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -4t + t2 = 0 + -0.6666666667
-4t + t2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-4t + t2 = -0.6666666667

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -0.6666666667 + 4

Reorder the terms:
4 + -4t + t2 = -0.6666666667 + 4

Combine like terms: -0.6666666667 + 4 = 3.3333333333
4 + -4t + t2 = 3.3333333333

Factor a perfect square on the left side:
(t + -2)(t + -2) = 3.3333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(t + -2) equal to 1.825741858 and -1.825741858.

Subproblem 1

t + -2 = 1.825741858 Simplifying t + -2 = 1.825741858 Reorder the terms: -2 + t = 1.825741858 Solving -2 + t = 1.825741858 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.825741858 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.825741858 + 2 t = 1.825741858 + 2 Combine like terms: 1.825741858 + 2 = 3.825741858 t = 3.825741858 Simplifying t = 3.825741858

Subproblem 2

t + -2 = -1.825741858 Simplifying t + -2 = -1.825741858 Reorder the terms: -2 + t = -1.825741858 Solving -2 + t = -1.825741858 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.825741858 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.825741858 + 2 t = -1.825741858 + 2 Combine like terms: -1.825741858 + 2 = 0.174258142 t = 0.174258142 Simplifying t = 0.174258142

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.825741858, 0.174258142}

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