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Simplifying 35 = -5t2 + 64t Reorder the terms: 35 = 64t + -5t2 Solving 35 = 64t + -5t2 Solving for variable 't'. Reorder the terms: 35 + -64t + 5t2 = 64t + -64t + -5t2 + 5t2 Combine like terms: 64t + -64t = 0 35 + -64t + 5t2 = 0 + -5t2 + 5t2 35 + -64t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 35 + -64t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7 + -12.8t + t2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -12.8t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -12.8t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -12.8t + t2 = 0 + -7 -12.8t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -12.8t + t2 = -7 The t term is -12.8t. Take half its coefficient (-6.4). Square it (40.96) and add it to both sides. Add '40.96' to each side of the equation. -12.8t + 40.96 + t2 = -7 + 40.96 Reorder the terms: 40.96 + -12.8t + t2 = -7 + 40.96 Combine like terms: -7 + 40.96 = 33.96 40.96 + -12.8t + t2 = 33.96 Factor a perfect square on the left side: (t + -6.4)(t + -6.4) = 33.96 Calculate the square root of the right side: 5.827520914 Break this problem into two subproblems by setting (t + -6.4) equal to 5.827520914 and -5.827520914.Subproblem 1
t + -6.4 = 5.827520914 Simplifying t + -6.4 = 5.827520914 Reorder the terms: -6.4 + t = 5.827520914 Solving -6.4 + t = 5.827520914 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.4' to each side of the equation. -6.4 + 6.4 + t = 5.827520914 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + t = 5.827520914 + 6.4 t = 5.827520914 + 6.4 Combine like terms: 5.827520914 + 6.4 = 12.227520914 t = 12.227520914 Simplifying t = 12.227520914Subproblem 2
t + -6.4 = -5.827520914 Simplifying t + -6.4 = -5.827520914 Reorder the terms: -6.4 + t = -5.827520914 Solving -6.4 + t = -5.827520914 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.4' to each side of the equation. -6.4 + 6.4 + t = -5.827520914 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + t = -5.827520914 + 6.4 t = -5.827520914 + 6.4 Combine like terms: -5.827520914 + 6.4 = 0.572479086 t = 0.572479086 Simplifying t = 0.572479086Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.227520914, 0.572479086}
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