0=16t^2+24t+20

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Solution for 0=16t^2+24t+20 equation:


Simplifying
0 = 16t2 + 24t + 20

Reorder the terms:
0 = 20 + 24t + 16t2

Solving
0 = 20 + 24t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -20 = -20
-20 + -24t + -16t2 = 20 + 24t + 16t2 + -20 + -24t + -16t2

Reorder the terms:
-20 + -24t + -16t2 = 20 + -20 + 24t + -24t + 16t2 + -16t2

Combine like terms: 20 + -20 = 0
-20 + -24t + -16t2 = 0 + 24t + -24t + 16t2 + -16t2
-20 + -24t + -16t2 = 24t + -24t + 16t2 + -16t2

Combine like terms: 24t + -24t = 0
-20 + -24t + -16t2 = 0 + 16t2 + -16t2
-20 + -24t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-20 + -24t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(5 + 6t + 4t2) = 0

Ignore the factor -4.

Subproblem 1

Set the factor '(5 + 6t + 4t2)' equal to zero and attempt to solve: Simplifying 5 + 6t + 4t2 = 0 Solving 5 + 6t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 1.5t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 1.5t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 1.5t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 1.5t + t2 = 0 + -1.25 1.5t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 1.5t + t2 = -1.25 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = -1.25 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = -1.25 + 0.5625 Combine like terms: -1.25 + 0.5625 = -0.6875 0.5625 + 1.5t + t2 = -0.6875 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = -0.6875 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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