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Simplifying 0 = 16t2 + 112t + 960 Reorder the terms: 0 = 960 + 112t + 16t2 Solving 0 = 960 + 112t + 16t2 Solving for variable 't'. Combine like terms: 0 + -960 = -960 -960 + -112t + -16t2 = 960 + 112t + 16t2 + -960 + -112t + -16t2 Reorder the terms: -960 + -112t + -16t2 = 960 + -960 + 112t + -112t + 16t2 + -16t2 Combine like terms: 960 + -960 = 0 -960 + -112t + -16t2 = 0 + 112t + -112t + 16t2 + -16t2 -960 + -112t + -16t2 = 112t + -112t + 16t2 + -16t2 Combine like terms: 112t + -112t = 0 -960 + -112t + -16t2 = 0 + 16t2 + -16t2 -960 + -112t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -960 + -112t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(60 + 7t + t2) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(60 + 7t + t2)' equal to zero and attempt to solve: Simplifying 60 + 7t + t2 = 0 Solving 60 + 7t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 7t + -60 + t2 = 0 + -60 Reorder the terms: 60 + -60 + 7t + t2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 7t + t2 = 0 + -60 7t + t2 = 0 + -60 Combine like terms: 0 + -60 = -60 7t + t2 = -60 The t term is 7t. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7t + 12.25 + t2 = -60 + 12.25 Reorder the terms: 12.25 + 7t + t2 = -60 + 12.25 Combine like terms: -60 + 12.25 = -47.75 12.25 + 7t + t2 = -47.75 Factor a perfect square on the left side: (t + 3.5)(t + 3.5) = -47.75 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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