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Simplifying t = -16t2 + 2304 Reorder the terms: t = 2304 + -16t2 Solving t = 2304 + -16t2 Solving for variable 't'. Reorder the terms: -2304 + t + 16t2 = 2304 + -16t2 + -2304 + 16t2 Reorder the terms: -2304 + t + 16t2 = 2304 + -2304 + -16t2 + 16t2 Combine like terms: 2304 + -2304 = 0 -2304 + t + 16t2 = 0 + -16t2 + 16t2 -2304 + t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2304 + t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -144 + 0.0625t + t2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 0.0625t + 144 + t2 = 0 + 144 Reorder the terms: -144 + 144 + 0.0625t + t2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 0.0625t + t2 = 0 + 144 0.0625t + t2 = 0 + 144 Combine like terms: 0 + 144 = 144 0.0625t + t2 = 144 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0625t + 0.25 + t2 = 144 + 0.25 Reorder the terms: 0.25 + 0.0625t + t2 = 144 + 0.25 Combine like terms: 144 + 0.25 = 144.25 0.25 + 0.0625t + t2 = 144.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (t + 0.5) equal to 12.010412149 and -12.010412149.Subproblem 1
t + 0.5 = 12.010412149 Simplifying t + 0.5 = 12.010412149 Reorder the terms: 0.5 + t = 12.010412149 Solving 0.5 + t = 12.010412149 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 12.010412149 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 12.010412149 + -0.5 t = 12.010412149 + -0.5 Combine like terms: 12.010412149 + -0.5 = 11.510412149 t = 11.510412149 Simplifying t = 11.510412149Subproblem 2
t + 0.5 = -12.010412149 Simplifying t + 0.5 = -12.010412149 Reorder the terms: 0.5 + t = -12.010412149 Solving 0.5 + t = -12.010412149 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -12.010412149 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -12.010412149 + -0.5 t = -12.010412149 + -0.5 Combine like terms: -12.010412149 + -0.5 = -12.510412149 t = -12.510412149 Simplifying t = -12.510412149Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.510412149, -12.510412149}
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