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Simplifying 0 = -16t(t) + 35t + -2.5 Multiply t * t 0 = -16t2 + 35t + -2.5 Reorder the terms: 0 = -2.5 + 35t + -16t2 Solving 0 = -2.5 + 35t + -16t2 Solving for variable 't'. Combine like terms: 0 + 2.5 = 2.5 2.5 + -35t + 16t2 = -2.5 + 35t + -16t2 + 2.5 + -35t + 16t2 Reorder the terms: 2.5 + -35t + 16t2 = -2.5 + 2.5 + 35t + -35t + -16t2 + 16t2 Combine like terms: -2.5 + 2.5 = 0.0 2.5 + -35t + 16t2 = 0.0 + 35t + -35t + -16t2 + 16t2 2.5 + -35t + 16t2 = 35t + -35t + -16t2 + 16t2 Combine like terms: 35t + -35t = 0 2.5 + -35t + 16t2 = 0 + -16t2 + 16t2 2.5 + -35t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 2.5 + -35t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.15625 + -2.1875t + t2 = 0 Move the constant term to the right: Add '-0.15625' to each side of the equation. 0.15625 + -2.1875t + -0.15625 + t2 = 0 + -0.15625 Reorder the terms: 0.15625 + -0.15625 + -2.1875t + t2 = 0 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + -2.1875t + t2 = 0 + -0.15625 -2.1875t + t2 = 0 + -0.15625 Combine like terms: 0 + -0.15625 = -0.15625 -2.1875t + t2 = -0.15625 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 = -0.15625 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875t + t2 = -0.15625 + 1.196289063 Combine like terms: -0.15625 + 1.196289063 = 1.040039063 1.196289063 + -2.1875t + t2 = 1.040039063 Factor a perfect square on the left side: (t + -1.09375)(t + -1.09375) = 1.040039063 Calculate the square root of the right side: 1.019823055 Break this problem into two subproblems by setting (t + -1.09375) equal to 1.019823055 and -1.019823055.Subproblem 1
t + -1.09375 = 1.019823055 Simplifying t + -1.09375 = 1.019823055 Reorder the terms: -1.09375 + t = 1.019823055 Solving -1.09375 + t = 1.019823055 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 = 1.019823055 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 1.019823055 + 1.09375 t = 1.019823055 + 1.09375 Combine like terms: 1.019823055 + 1.09375 = 2.113573055 t = 2.113573055 Simplifying t = 2.113573055Subproblem 2
t + -1.09375 = -1.019823055 Simplifying t + -1.09375 = -1.019823055 Reorder the terms: -1.09375 + t = -1.019823055 Solving -1.09375 + t = -1.019823055 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 = -1.019823055 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -1.019823055 + 1.09375 t = -1.019823055 + 1.09375 Combine like terms: -1.019823055 + 1.09375 = 0.073926945 t = 0.073926945 Simplifying t = 0.073926945Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.113573055, 0.073926945}
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