3t^2-44t+45=0

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Solution for 3t^2-44t+45=0 equation:


Simplifying
3t2 + -44t + 45 = 0

Reorder the terms:
45 + -44t + 3t2 = 0

Solving
45 + -44t + 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'.
15 + -14.66666667t + t2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -14.66666667t + -15 + t2 = 0 + -15

Reorder the terms:
15 + -15 + -14.66666667t + t2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -14.66666667t + t2 = 0 + -15
-14.66666667t + t2 = 0 + -15

Combine like terms: 0 + -15 = -15
-14.66666667t + t2 = -15

The t term is -14.66666667t.  Take half its coefficient (-7.333333335).
Square it (53.77777780) and add it to both sides.

Add '53.77777780' to each side of the equation.
-14.66666667t + 53.77777780 + t2 = -15 + 53.77777780

Reorder the terms:
53.77777780 + -14.66666667t + t2 = -15 + 53.77777780

Combine like terms: -15 + 53.77777780 = 38.7777778
53.77777780 + -14.66666667t + t2 = 38.7777778

Factor a perfect square on the left side:
(t + -7.333333335)(t + -7.333333335) = 38.7777778

Calculate the square root of the right side: 6.227180566

Break this problem into two subproblems by setting 
(t + -7.333333335) equal to 6.227180566 and -6.227180566.

Subproblem 1

t + -7.333333335 = 6.227180566 Simplifying t + -7.333333335 = 6.227180566 Reorder the terms: -7.333333335 + t = 6.227180566 Solving -7.333333335 + t = 6.227180566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + t = 6.227180566 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + t = 6.227180566 + 7.333333335 t = 6.227180566 + 7.333333335 Combine like terms: 6.227180566 + 7.333333335 = 13.560513901 t = 13.560513901 Simplifying t = 13.560513901

Subproblem 2

t + -7.333333335 = -6.227180566 Simplifying t + -7.333333335 = -6.227180566 Reorder the terms: -7.333333335 + t = -6.227180566 Solving -7.333333335 + t = -6.227180566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + t = -6.227180566 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + t = -6.227180566 + 7.333333335 t = -6.227180566 + 7.333333335 Combine like terms: -6.227180566 + 7.333333335 = 1.106152769 t = 1.106152769 Simplifying t = 1.106152769

Solution

The solution to the problem is based on the solutions from the subproblems. t = {13.560513901, 1.106152769}

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