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Simplifying 0 = -16t2 + t + 100 Reorder the terms: 0 = 100 + t + -16t2 Solving 0 = 100 + t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -1t + 16t2 = 100 + t + -16t2 + -100 + -1t + 16t2 Reorder the terms: -100 + -1t + 16t2 = 100 + -100 + t + -1t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + -1t + 16t2 = 0 + t + -1t + -16t2 + 16t2 -100 + -1t + 16t2 = t + -1t + -16t2 + 16t2 Combine like terms: t + -1t = 0 -100 + -1t + 16t2 = 0 + -16t2 + 16t2 -100 + -1t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -1t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.25 + -0.0625t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -0.0625t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -0.0625t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -0.0625t + t2 = 0 + 6.25 -0.0625t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -0.0625t + t2 = 6.25 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 = 6.25 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625t + t2 = 6.25 + 0.0009765625 Combine like terms: 6.25 + 0.0009765625 = 6.2509765625 0.0009765625 + -0.0625t + t2 = 6.2509765625 Factor a perfect square on the left side: (t + -0.03125)(t + -0.03125) = 6.2509765625 Calculate the square root of the right side: 2.500195305 Break this problem into two subproblems by setting (t + -0.03125) equal to 2.500195305 and -2.500195305.Subproblem 1
t + -0.03125 = 2.500195305 Simplifying t + -0.03125 = 2.500195305 Reorder the terms: -0.03125 + t = 2.500195305 Solving -0.03125 + t = 2.500195305 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 = 2.500195305 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = 2.500195305 + 0.03125 t = 2.500195305 + 0.03125 Combine like terms: 2.500195305 + 0.03125 = 2.531445305 t = 2.531445305 Simplifying t = 2.531445305Subproblem 2
t + -0.03125 = -2.500195305 Simplifying t + -0.03125 = -2.500195305 Reorder the terms: -0.03125 + t = -2.500195305 Solving -0.03125 + t = -2.500195305 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 = -2.500195305 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = -2.500195305 + 0.03125 t = -2.500195305 + 0.03125 Combine like terms: -2.500195305 + 0.03125 = -2.468945305 t = -2.468945305 Simplifying t = -2.468945305Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.531445305, -2.468945305}
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