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Simplifying 0 = -16t2 + t + 144 Reorder the terms: 0 = 144 + t + -16t2 Solving 0 = 144 + t + -16t2 Solving for variable 't'. Combine like terms: 0 + -144 = -144 -144 + -1t + 16t2 = 144 + t + -16t2 + -144 + -1t + 16t2 Reorder the terms: -144 + -1t + 16t2 = 144 + -144 + t + -1t + -16t2 + 16t2 Combine like terms: 144 + -144 = 0 -144 + -1t + 16t2 = 0 + t + -1t + -16t2 + 16t2 -144 + -1t + 16t2 = t + -1t + -16t2 + 16t2 Combine like terms: t + -1t = 0 -144 + -1t + 16t2 = 0 + -16t2 + 16t2 -144 + -1t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -144 + -1t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9 + -0.0625t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.0625t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -0.0625t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.0625t + t2 = 0 + 9 -0.0625t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.0625t + t2 = 9 The t term is -0.0625t. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625t + 0.0009765625 + t2 = 9 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625t + t2 = 9 + 0.0009765625 Combine like terms: 9 + 0.0009765625 = 9.0009765625 0.0009765625 + -0.0625t + t2 = 9.0009765625 Factor a perfect square on the left side: (t + -0.03125)(t + -0.03125) = 9.0009765625 Calculate the square root of the right side: 3.000162756 Break this problem into two subproblems by setting (t + -0.03125) equal to 3.000162756 and -3.000162756.Subproblem 1
t + -0.03125 = 3.000162756 Simplifying t + -0.03125 = 3.000162756 Reorder the terms: -0.03125 + t = 3.000162756 Solving -0.03125 + t = 3.000162756 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + t = 3.000162756 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = 3.000162756 + 0.03125 t = 3.000162756 + 0.03125 Combine like terms: 3.000162756 + 0.03125 = 3.031412756 t = 3.031412756 Simplifying t = 3.031412756Subproblem 2
t + -0.03125 = -3.000162756 Simplifying t + -0.03125 = -3.000162756 Reorder the terms: -0.03125 + t = -3.000162756 Solving -0.03125 + t = -3.000162756 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + t = -3.000162756 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = -3.000162756 + 0.03125 t = -3.000162756 + 0.03125 Combine like terms: -3.000162756 + 0.03125 = -2.968912756 t = -2.968912756 Simplifying t = -2.968912756Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.031412756, -2.968912756}
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