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Simplifying 0 = -16t2 + 5t + 92 Reorder the terms: 0 = 92 + 5t + -16t2 Solving 0 = 92 + 5t + -16t2 Solving for variable 't'. Combine like terms: 0 + -92 = -92 -92 + -5t + 16t2 = 92 + 5t + -16t2 + -92 + -5t + 16t2 Reorder the terms: -92 + -5t + 16t2 = 92 + -92 + 5t + -5t + -16t2 + 16t2 Combine like terms: 92 + -92 = 0 -92 + -5t + 16t2 = 0 + 5t + -5t + -16t2 + 16t2 -92 + -5t + 16t2 = 5t + -5t + -16t2 + 16t2 Combine like terms: 5t + -5t = 0 -92 + -5t + 16t2 = 0 + -16t2 + 16t2 -92 + -5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -92 + -5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.75 + -0.3125t + t2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -0.3125t + 5.75 + t2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -0.3125t + t2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -0.3125t + t2 = 0 + 5.75 -0.3125t + t2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -0.3125t + t2 = 5.75 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 = 5.75 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 5.75 + 0.0244140625 Combine like terms: 5.75 + 0.0244140625 = 5.7744140625 0.0244140625 + -0.3125t + t2 = 5.7744140625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 5.7744140625 Calculate the square root of the right side: 2.403001053 Break this problem into two subproblems by setting (t + -0.15625) equal to 2.403001053 and -2.403001053.Subproblem 1
t + -0.15625 = 2.403001053 Simplifying t + -0.15625 = 2.403001053 Reorder the terms: -0.15625 + t = 2.403001053 Solving -0.15625 + t = 2.403001053 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 = 2.403001053 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 2.403001053 + 0.15625 t = 2.403001053 + 0.15625 Combine like terms: 2.403001053 + 0.15625 = 2.559251053 t = 2.559251053 Simplifying t = 2.559251053Subproblem 2
t + -0.15625 = -2.403001053 Simplifying t + -0.15625 = -2.403001053 Reorder the terms: -0.15625 + t = -2.403001053 Solving -0.15625 + t = -2.403001053 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 = -2.403001053 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -2.403001053 + 0.15625 t = -2.403001053 + 0.15625 Combine like terms: -2.403001053 + 0.15625 = -2.246751053 t = -2.246751053 Simplifying t = -2.246751053Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.559251053, -2.246751053}
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