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Simplifying 0 = -16t2 + 35t + 15 Reorder the terms: 0 = 15 + 35t + -16t2 Solving 0 = 15 + 35t + -16t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -35t + 16t2 = 15 + 35t + -16t2 + -15 + -35t + 16t2 Reorder the terms: -15 + -35t + 16t2 = 15 + -15 + 35t + -35t + -16t2 + 16t2 Combine like terms: 15 + -15 = 0 -15 + -35t + 16t2 = 0 + 35t + -35t + -16t2 + 16t2 -15 + -35t + 16t2 = 35t + -35t + -16t2 + 16t2 Combine like terms: 35t + -35t = 0 -15 + -35t + 16t2 = 0 + -16t2 + 16t2 -15 + -35t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -15 + -35t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -2.1875t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -2.1875t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -2.1875t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -2.1875t + t2 = 0 + 0.9375 -2.1875t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -2.1875t + t2 = 0.9375 The t term is -2.1875t. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875t + 1.196289063 + t2 = 0.9375 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875t + t2 = 0.9375 + 1.196289063 Combine like terms: 0.9375 + 1.196289063 = 2.133789063 1.196289063 + -2.1875t + t2 = 2.133789063 Factor a perfect square on the left side: (t + -1.09375)(t + -1.09375) = 2.133789063 Calculate the square root of the right side: 1.460749487 Break this problem into two subproblems by setting (t + -1.09375) equal to 1.460749487 and -1.460749487.Subproblem 1
t + -1.09375 = 1.460749487 Simplifying t + -1.09375 = 1.460749487 Reorder the terms: -1.09375 + t = 1.460749487 Solving -1.09375 + t = 1.460749487 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = 1.460749487 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 1.460749487 + 1.09375 t = 1.460749487 + 1.09375 Combine like terms: 1.460749487 + 1.09375 = 2.554499487 t = 2.554499487 Simplifying t = 2.554499487Subproblem 2
t + -1.09375 = -1.460749487 Simplifying t + -1.09375 = -1.460749487 Reorder the terms: -1.09375 + t = -1.460749487 Solving -1.09375 + t = -1.460749487 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = -1.460749487 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -1.460749487 + 1.09375 t = -1.460749487 + 1.09375 Combine like terms: -1.460749487 + 1.09375 = -0.366999487 t = -0.366999487 Simplifying t = -0.366999487Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.554499487, -0.366999487}
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