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Simplifying 0 = -16t2 + -5t + 100 Reorder the terms: 0 = 100 + -5t + -16t2 Solving 0 = 100 + -5t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + 5t + 16t2 = 100 + -5t + -16t2 + -100 + 5t + 16t2 Reorder the terms: -100 + 5t + 16t2 = 100 + -100 + -5t + 5t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + 5t + 16t2 = 0 + -5t + 5t + -16t2 + 16t2 -100 + 5t + 16t2 = -5t + 5t + -16t2 + 16t2 Combine like terms: -5t + 5t = 0 -100 + 5t + 16t2 = 0 + -16t2 + 16t2 -100 + 5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + 5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.25 + 0.3125t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 0.3125t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 0.3125t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 0.3125t + t2 = 0 + 6.25 0.3125t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 0.3125t + t2 = 6.25 The t term is 0.3125t. Take half its coefficient (0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. 0.3125t + 0.0244140625 + t2 = 6.25 + 0.0244140625 Reorder the terms: 0.0244140625 + 0.3125t + t2 = 6.25 + 0.0244140625 Combine like terms: 6.25 + 0.0244140625 = 6.2744140625 0.0244140625 + 0.3125t + t2 = 6.2744140625 Factor a perfect square on the left side: (t + 0.15625)(t + 0.15625) = 6.2744140625 Calculate the square root of the right side: 2.504878053 Break this problem into two subproblems by setting (t + 0.15625) equal to 2.504878053 and -2.504878053.Subproblem 1
t + 0.15625 = 2.504878053 Simplifying t + 0.15625 = 2.504878053 Reorder the terms: 0.15625 + t = 2.504878053 Solving 0.15625 + t = 2.504878053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + t = 2.504878053 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + t = 2.504878053 + -0.15625 t = 2.504878053 + -0.15625 Combine like terms: 2.504878053 + -0.15625 = 2.348628053 t = 2.348628053 Simplifying t = 2.348628053Subproblem 2
t + 0.15625 = -2.504878053 Simplifying t + 0.15625 = -2.504878053 Reorder the terms: 0.15625 + t = -2.504878053 Solving 0.15625 + t = -2.504878053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + t = -2.504878053 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + t = -2.504878053 + -0.15625 t = -2.504878053 + -0.15625 Combine like terms: -2.504878053 + -0.15625 = -2.661128053 t = -2.661128053 Simplifying t = -2.661128053Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.348628053, -2.661128053}
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