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Simplifying 16t2 + 32t + 768 = 0 Reorder the terms: 768 + 32t + 16t2 = 0 Solving 768 + 32t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(48 + 2t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(48 + 2t + t2)' equal to zero and attempt to solve: Simplifying 48 + 2t + t2 = 0 Solving 48 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + 2t + -48 + t2 = 0 + -48 Reorder the terms: 48 + -48 + 2t + t2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 2t + t2 = 0 + -48 2t + t2 = 0 + -48 Combine like terms: 0 + -48 = -48 2t + t2 = -48 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 = -48 + 1 Reorder the terms: 1 + 2t + t2 = -48 + 1 Combine like terms: -48 + 1 = -47 1 + 2t + t2 = -47 Factor a perfect square on the left side: (t + 1)(t + 1) = -47 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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