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Simplifying 16t2 + 32t + 256 = 0 Reorder the terms: 256 + 32t + 16t2 = 0 Solving 256 + 32t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(16 + 2t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(16 + 2t + t2)' equal to zero and attempt to solve: Simplifying 16 + 2t + t2 = 0 Solving 16 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 2t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + 2t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 2t + t2 = 0 + -16 2t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 2t + t2 = -16 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 = -16 + 1 Reorder the terms: 1 + 2t + t2 = -16 + 1 Combine like terms: -16 + 1 = -15 1 + 2t + t2 = -15 Factor a perfect square on the left side: (t + 1)(t + 1) = -15 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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