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Simplifying 16t2 + 128t + 320 = 0 Reorder the terms: 320 + 128t + 16t2 = 0 Solving 320 + 128t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(20 + 8t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(20 + 8t + t2)' equal to zero and attempt to solve: Simplifying 20 + 8t + t2 = 0 Solving 20 + 8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 8t + -20 + t2 = 0 + -20 Reorder the terms: 20 + -20 + 8t + t2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 8t + t2 = 0 + -20 8t + t2 = 0 + -20 Combine like terms: 0 + -20 = -20 8t + t2 = -20 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 = -20 + 16 Reorder the terms: 16 + 8t + t2 = -20 + 16 Combine like terms: -20 + 16 = -4 16 + 8t + t2 = -4 Factor a perfect square on the left side: (t + 4)(t + 4) = -4 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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