55=-5t^2+30t+5

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Solution for 55=-5t^2+30t+5 equation: 


Simplifying
55 = -5t2 + 30t + 5

Reorder the terms:
55 = 5 + 30t + -5t2

Solving
55 = 5 + 30t + -5t2

Solving for variable 't'.

Combine like terms: 55 + -5 = 50
50 + -30t + 5t2 = 5 + 30t + -5t2 + -5 + -30t + 5t2

Reorder the terms:
50 + -30t + 5t2 = 5 + -5 + 30t + -30t + -5t2 + 5t2

Combine like terms: 5 + -5 = 0
50 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2
50 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2

Combine like terms: 30t + -30t = 0
50 + -30t + 5t2 = 0 + -5t2 + 5t2
50 + -30t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
50 + -30t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(10 + -6t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(10 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
10 + -6t + t2 = 0

Solving
10 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -6t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + -6t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -6t + t2 = 0 + -10
-6t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
-6t + t2 = -10

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 = -10 + 9

Reorder the terms:
9 + -6t + t2 = -10 + 9

Combine like terms: -10 + 9 = -1
9 + -6t + t2 = -1

Factor a perfect square on the left side:
(t + -3)(t + -3) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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