30=-16t^2+44t-24

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Solution for 30=-16t^2+44t-24 equation:


Simplifying
30 = -16t2 + 44t + -24

Reorder the terms:
30 = -24 + 44t + -16t2

Solving
30 = -24 + 44t + -16t2

Solving for variable 't'.

Combine like terms: 30 + 24 = 54
54 + -44t + 16t2 = -24 + 44t + -16t2 + 24 + -44t + 16t2

Reorder the terms:
54 + -44t + 16t2 = -24 + 24 + 44t + -44t + -16t2 + 16t2

Combine like terms: -24 + 24 = 0
54 + -44t + 16t2 = 0 + 44t + -44t + -16t2 + 16t2
54 + -44t + 16t2 = 44t + -44t + -16t2 + 16t2

Combine like terms: 44t + -44t = 0
54 + -44t + 16t2 = 0 + -16t2 + 16t2
54 + -44t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
54 + -44t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -22t + 8t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(27 + -22t + 8t2)' equal to zero and attempt to solve: Simplifying 27 + -22t + 8t2 = 0 Solving 27 + -22t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.375 + -2.75t + t2 = 0 Move the constant term to the right: Add '-3.375' to each side of the equation. 3.375 + -2.75t + -3.375 + t2 = 0 + -3.375 Reorder the terms: 3.375 + -3.375 + -2.75t + t2 = 0 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + -2.75t + t2 = 0 + -3.375 -2.75t + t2 = 0 + -3.375 Combine like terms: 0 + -3.375 = -3.375 -2.75t + t2 = -3.375 The t term is -2.75t. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75t + 1.890625 + t2 = -3.375 + 1.890625 Reorder the terms: 1.890625 + -2.75t + t2 = -3.375 + 1.890625 Combine like terms: -3.375 + 1.890625 = -1.484375 1.890625 + -2.75t + t2 = -1.484375 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = -1.484375 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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