2t^2-12t+9=0

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Solution for 2t^2-12t+9=0 equation:


Simplifying
2t2 + -12t + 9 = 0

Reorder the terms:
9 + -12t + 2t2 = 0

Solving
9 + -12t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
4.5 + -6t + t2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -6t + -4.5 + t2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -6t + t2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -6t + t2 = 0 + -4.5
-6t + t2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-6t + t2 = -4.5

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 = -4.5 + 9

Reorder the terms:
9 + -6t + t2 = -4.5 + 9

Combine like terms: -4.5 + 9 = 4.5
9 + -6t + t2 = 4.5

Factor a perfect square on the left side:
(t + -3)(t + -3) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(t + -3) equal to 2.121320344 and -2.121320344.

Subproblem 1

t + -3 = 2.121320344 Simplifying t + -3 = 2.121320344 Reorder the terms: -3 + t = 2.121320344 Solving -3 + t = 2.121320344 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 = 2.121320344 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.121320344 + 3 t = 2.121320344 + 3 Combine like terms: 2.121320344 + 3 = 5.121320344 t = 5.121320344 Simplifying t = 5.121320344

Subproblem 2

t + -3 = -2.121320344 Simplifying t + -3 = -2.121320344 Reorder the terms: -3 + t = -2.121320344 Solving -3 + t = -2.121320344 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 = -2.121320344 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.121320344 + 3 t = -2.121320344 + 3 Combine like terms: -2.121320344 + 3 = 0.878679656 t = 0.878679656 Simplifying t = 0.878679656

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.121320344, 0.878679656}

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