0=16t^2+128t+768

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Solution for 0=16t^2+128t+768 equation:


Simplifying
0 = 16t2 + 128t + 768

Reorder the terms:
0 = 768 + 128t + 16t2

Solving
0 = 768 + 128t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -768 = -768
-768 + -128t + -16t2 = 768 + 128t + 16t2 + -768 + -128t + -16t2

Reorder the terms:
-768 + -128t + -16t2 = 768 + -768 + 128t + -128t + 16t2 + -16t2

Combine like terms: 768 + -768 = 0
-768 + -128t + -16t2 = 0 + 128t + -128t + 16t2 + -16t2
-768 + -128t + -16t2 = 128t + -128t + 16t2 + -16t2

Combine like terms: 128t + -128t = 0
-768 + -128t + -16t2 = 0 + 16t2 + -16t2
-768 + -128t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-768 + -128t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-16'.
-16(48 + 8t + t2) = 0

Ignore the factor -16.

Subproblem 1

Set the factor '(48 + 8t + t2)' equal to zero and attempt to solve: Simplifying 48 + 8t + t2 = 0 Solving 48 + 8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + 8t + -48 + t2 = 0 + -48 Reorder the terms: 48 + -48 + 8t + t2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 8t + t2 = 0 + -48 8t + t2 = 0 + -48 Combine like terms: 0 + -48 = -48 8t + t2 = -48 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = -48 + 16 Reorder the terms: 16 + 8t + t2 = -48 + 16 Combine like terms: -48 + 16 = -32 16 + 8t + t2 = -32 Factor a perfect square on the left side: (t + 4)(t + 4) = -32 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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