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Simplifying 0 = 16t2 + 80t + 384 Reorder the terms: 0 = 384 + 80t + 16t2 Solving 0 = 384 + 80t + 16t2 Solving for variable 't'. Combine like terms: 0 + -384 = -384 -384 + -80t + -16t2 = 384 + 80t + 16t2 + -384 + -80t + -16t2 Reorder the terms: -384 + -80t + -16t2 = 384 + -384 + 80t + -80t + 16t2 + -16t2 Combine like terms: 384 + -384 = 0 -384 + -80t + -16t2 = 0 + 80t + -80t + 16t2 + -16t2 -384 + -80t + -16t2 = 80t + -80t + 16t2 + -16t2 Combine like terms: 80t + -80t = 0 -384 + -80t + -16t2 = 0 + 16t2 + -16t2 -384 + -80t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -384 + -80t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(24 + 5t + t2) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(24 + 5t + t2)' equal to zero and attempt to solve: Simplifying 24 + 5t + t2 = 0 Solving 24 + 5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 5t + -24 + t2 = 0 + -24 Reorder the terms: 24 + -24 + 5t + t2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 5t + t2 = 0 + -24 5t + t2 = 0 + -24 Combine like terms: 0 + -24 = -24 5t + t2 = -24 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = -24 + 6.25 Reorder the terms: 6.25 + 5t + t2 = -24 + 6.25 Combine like terms: -24 + 6.25 = -17.75 6.25 + 5t + t2 = -17.75 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = -17.75 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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