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Simplifying 16t2 + 32t + 384 = 0 Reorder the terms: 384 + 32t + 16t2 = 0 Solving 384 + 32t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(24 + 2t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(24 + 2t + t2)' equal to zero and attempt to solve: Simplifying 24 + 2t + t2 = 0 Solving 24 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 2t + -24 + t2 = 0 + -24 Reorder the terms: 24 + -24 + 2t + t2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 2t + t2 = 0 + -24 2t + t2 = 0 + -24 Combine like terms: 0 + -24 = -24 2t + t2 = -24 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = -24 + 1 Reorder the terms: 1 + 2t + t2 = -24 + 1 Combine like terms: -24 + 1 = -23 1 + 2t + t2 = -23 Factor a perfect square on the left side: (t + 1)(t + 1) = -23 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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