33t^2-18t+2=0

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Solution for 33t^2-18t+2=0 equation:


Simplifying
33t2 + -18t + 2 = 0

Reorder the terms:
2 + -18t + 33t2 = 0

Solving
2 + -18t + 33t2 = 0

Solving for variable 't'.

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

Divide each side by '33'.
0.06060606061 + -0.5454545455t + t2 = 0

Move the constant term to the right:

Add '-0.06060606061' to each side of the equation.
0.06060606061 + -0.5454545455t + -0.06060606061 + t2 = 0 + -0.06060606061

Reorder the terms:
0.06060606061 + -0.06060606061 + -0.5454545455t + t2 = 0 + -0.06060606061

Combine like terms: 0.06060606061 + -0.06060606061 = 0.00000000000
0.00000000000 + -0.5454545455t + t2 = 0 + -0.06060606061
-0.5454545455t + t2 = 0 + -0.06060606061

Combine like terms: 0 + -0.06060606061 = -0.06060606061
-0.5454545455t + t2 = -0.06060606061

The t term is -0.5454545455t.  Take half its coefficient (-0.2727272728).
Square it (0.07438016533) and add it to both sides.

Add '0.07438016533' to each side of the equation.
-0.5454545455t + 0.07438016533 + t2 = -0.06060606061 + 0.07438016533

Reorder the terms:
0.07438016533 + -0.5454545455t + t2 = -0.06060606061 + 0.07438016533

Combine like terms: -0.06060606061 + 0.07438016533 = 0.01377410472
0.07438016533 + -0.5454545455t + t2 = 0.01377410472

Factor a perfect square on the left side:
(t + -0.2727272728)(t + -0.2727272728) = 0.01377410472

Calculate the square root of the right side: 0.117363132

Break this problem into two subproblems by setting 
(t + -0.2727272728) equal to 0.117363132 and -0.117363132.

Subproblem 1

t + -0.2727272728 = 0.117363132 Simplifying t + -0.2727272728 = 0.117363132 Reorder the terms: -0.2727272728 + t = 0.117363132 Solving -0.2727272728 + t = 0.117363132 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + t = 0.117363132 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + t = 0.117363132 + 0.2727272728 t = 0.117363132 + 0.2727272728 Combine like terms: 0.117363132 + 0.2727272728 = 0.3900904048 t = 0.3900904048 Simplifying t = 0.3900904048

Subproblem 2

t + -0.2727272728 = -0.117363132 Simplifying t + -0.2727272728 = -0.117363132 Reorder the terms: -0.2727272728 + t = -0.117363132 Solving -0.2727272728 + t = -0.117363132 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + t = -0.117363132 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + t = -0.117363132 + 0.2727272728 t = -0.117363132 + 0.2727272728 Combine like terms: -0.117363132 + 0.2727272728 = 0.1553641408 t = 0.1553641408 Simplifying t = 0.1553641408

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.3900904048, 0.1553641408}

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