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Simplifying 0 = -16t2 + 100t + 29 Reorder the terms: 0 = 29 + 100t + -16t2 Solving 0 = 29 + 100t + -16t2 Solving for variable 't'. Combine like terms: 0 + -29 = -29 -29 + -100t + 16t2 = 29 + 100t + -16t2 + -29 + -100t + 16t2 Reorder the terms: -29 + -100t + 16t2 = 29 + -29 + 100t + -100t + -16t2 + 16t2 Combine like terms: 29 + -29 = 0 -29 + -100t + 16t2 = 0 + 100t + -100t + -16t2 + 16t2 -29 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 -29 + -100t + 16t2 = 0 + -16t2 + 16t2 -29 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -29 + -100t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.8125 + -6.25t + t2 = 0 Move the constant term to the right: Add '1.8125' to each side of the equation. -1.8125 + -6.25t + 1.8125 + t2 = 0 + 1.8125 Reorder the terms: -1.8125 + 1.8125 + -6.25t + t2 = 0 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + -6.25t + t2 = 0 + 1.8125 -6.25t + t2 = 0 + 1.8125 Combine like terms: 0 + 1.8125 = 1.8125 -6.25t + t2 = 1.8125 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = 1.8125 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = 1.8125 + 9.765625 Combine like terms: 1.8125 + 9.765625 = 11.578125 9.765625 + -6.25t + t2 = 11.578125 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 11.578125 Calculate the square root of the right side: 3.402664397 Break this problem into two subproblems by setting (t + -3.125) equal to 3.402664397 and -3.402664397.Subproblem 1
t + -3.125 = 3.402664397 Simplifying t + -3.125 = 3.402664397 Reorder the terms: -3.125 + t = 3.402664397 Solving -3.125 + t = 3.402664397 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 3.402664397 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 3.402664397 + 3.125 t = 3.402664397 + 3.125 Combine like terms: 3.402664397 + 3.125 = 6.527664397 t = 6.527664397 Simplifying t = 6.527664397Subproblem 2
t + -3.125 = -3.402664397 Simplifying t + -3.125 = -3.402664397 Reorder the terms: -3.125 + t = -3.402664397 Solving -3.125 + t = -3.402664397 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -3.402664397 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -3.402664397 + 3.125 t = -3.402664397 + 3.125 Combine like terms: -3.402664397 + 3.125 = -0.277664397 t = -0.277664397 Simplifying t = -0.277664397Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.527664397, -0.277664397}
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