3t^2+25t+45=0

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Solution for 3t^2+25t+45=0 equation: 


Simplifying
3t2 + 25t + 45 = 0

Reorder the terms:
45 + 25t + 3t2 = 0

Solving
45 + 25t + 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 + 8.333333333t + t2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 8.333333333t + -15 + t2 = 0 + -15

Reorder the terms:
15 + -15 + 8.333333333t + t2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 8.333333333t + t2 = 0 + -15
8.333333333t + t2 = 0 + -15

Combine like terms: 0 + -15 = -15
8.333333333t + t2 = -15

The t term is 8.333333333t.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333t + 17.36111111 + t2 = -15 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333t + t2 = -15 + 17.36111111

Combine like terms: -15 + 17.36111111 = 2.36111111
17.36111111 + 8.333333333t + t2 = 2.36111111

Factor a perfect square on the left side:
(t + 4.166666667)(t + 4.166666667) = 2.36111111

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(t + 4.166666667) equal to 1.536590743 and -1.536590743.


Subproblem 1
t + 4.166666667 = 1.536590743

Simplifying
t + 4.166666667 = 1.536590743

Reorder the terms:
4.166666667 + t = 1.536590743

Solving
4.166666667 + t = 1.536590743

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + t = 1.536590743 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + t = 1.536590743 + -4.166666667
t = 1.536590743 + -4.166666667

Combine like terms: 1.536590743 + -4.166666667 = -2.630075924
t = -2.630075924

Simplifying
t = -2.630075924


Subproblem 2
t + 4.166666667 = -1.536590743

Simplifying
t + 4.166666667 = -1.536590743

Reorder the terms:
4.166666667 + t = -1.536590743

Solving
4.166666667 + t = -1.536590743

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + t = -1.536590743 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + t = -1.536590743 + -4.166666667
t = -1.536590743 + -4.166666667

Combine like terms: -1.536590743 + -4.166666667 = -5.70325741
t = -5.70325741

Simplifying
t = -5.70325741


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-2.630075924, -5.70325741}

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