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Simplifying 2704t = 16t2 + 2704 Reorder the terms: 2704t = 2704 + 16t2 Solving 2704t = 2704 + 16t2 Solving for variable 't'. Reorder the terms: -2704 + 2704t + -16t2 = 2704 + 16t2 + -2704 + -16t2 Reorder the terms: -2704 + 2704t + -16t2 = 2704 + -2704 + 16t2 + -16t2 Combine like terms: 2704 + -2704 = 0 -2704 + 2704t + -16t2 = 0 + 16t2 + -16t2 -2704 + 2704t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -2704 + 2704t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-169 + 169t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-169 + 169t + -1t2)' equal to zero and attempt to solve: Simplifying -169 + 169t + -1t2 = 0 Solving -169 + 169t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 169 + -169t + t2 = 0 Move the constant term to the right: Add '-169' to each side of the equation. 169 + -169t + -169 + t2 = 0 + -169 Reorder the terms: 169 + -169 + -169t + t2 = 0 + -169 Combine like terms: 169 + -169 = 0 0 + -169t + t2 = 0 + -169 -169t + t2 = 0 + -169 Combine like terms: 0 + -169 = -169 -169t + t2 = -169 The t term is -169t. Take half its coefficient (-84.5). Square it (7140.25) and add it to both sides. Add '7140.25' to each side of the equation. -169t + 7140.25 + t2 = -169 + 7140.25 Reorder the terms: 7140.25 + -169t + t2 = -169 + 7140.25 Combine like terms: -169 + 7140.25 = 6971.25 7140.25 + -169t + t2 = 6971.25 Factor a perfect square on the left side: (t + -84.5)(t + -84.5) = 6971.25 Calculate the square root of the right side: 83.494011761 Break this problem into two subproblems by setting (t + -84.5) equal to 83.494011761 and -83.494011761.Subproblem 1
t + -84.5 = 83.494011761 Simplifying t + -84.5 = 83.494011761 Reorder the terms: -84.5 + t = 83.494011761 Solving -84.5 + t = 83.494011761 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '84.5' to each side of the equation. -84.5 + 84.5 + t = 83.494011761 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + t = 83.494011761 + 84.5 t = 83.494011761 + 84.5 Combine like terms: 83.494011761 + 84.5 = 167.994011761 t = 167.994011761 Simplifying t = 167.994011761Subproblem 2
t + -84.5 = -83.494011761 Simplifying t + -84.5 = -83.494011761 Reorder the terms: -84.5 + t = -83.494011761 Solving -84.5 + t = -83.494011761 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '84.5' to each side of the equation. -84.5 + 84.5 + t = -83.494011761 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + t = -83.494011761 + 84.5 t = -83.494011761 + 84.5 Combine like terms: -83.494011761 + 84.5 = 1.005988239 t = 1.005988239 Simplifying t = 1.005988239Solution
The solution to the problem is based on the solutions from the subproblems. t = {167.994011761, 1.005988239}Solution
t = {167.994011761, 1.005988239}
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