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Simplifying 85 = 40t + -5t2 Solving 85 = 40t + -5t2 Solving for variable 't'. Reorder the terms: 85 + -40t + 5t2 = 40t + -40t + -5t2 + 5t2 Combine like terms: 40t + -40t = 0 85 + -40t + 5t2 = 0 + -5t2 + 5t2 85 + -40t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 85 + -40t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(17 + -8t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(17 + -8t + t2)' equal to zero and attempt to solve: Simplifying 17 + -8t + t2 = 0 Solving 17 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -8t + -17 + t2 = 0 + -17 Reorder the terms: 17 + -17 + -8t + t2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -8t + t2 = 0 + -17 -8t + t2 = 0 + -17 Combine like terms: 0 + -17 = -17 -8t + t2 = -17 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 = -17 + 16 Reorder the terms: 16 + -8t + t2 = -17 + 16 Combine like terms: -17 + 16 = -1 16 + -8t + t2 = -1 Factor a perfect square on the left side: (t + -4)(t + -4) = -1 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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