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Simplifying 1.75t2 = 245 + 35t Solving 1.75t2 = 245 + 35t Solving for variable 't'. Reorder the terms: -245 + -35t + 1.75t2 = 245 + 35t + -245 + -35t Reorder the terms: -245 + -35t + 1.75t2 = 245 + -245 + 35t + -35t Combine like terms: 245 + -245 = 0 -245 + -35t + 1.75t2 = 0 + 35t + -35t -245 + -35t + 1.75t2 = 35t + -35t Combine like terms: 35t + -35t = 0 -245 + -35t + 1.75t2 = 0 Begin completing the square. Divide all terms by 1.75 the coefficient of the squared term: Divide each side by '1.75'. -140 + -20t + t2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + -20t + 140 + t2 = 0 + 140 Reorder the terms: -140 + 140 + -20t + t2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -20t + t2 = 0 + 140 -20t + t2 = 0 + 140 Combine like terms: 0 + 140 = 140 -20t + t2 = 140 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 140 + 100 Reorder the terms: 100 + -20t + t2 = 140 + 100 Combine like terms: 140 + 100 = 240 100 + -20t + t2 = 240 Factor a perfect square on the left side: (t + -10)(t + -10) = 240 Calculate the square root of the right side: 15.491933385 Break this problem into two subproblems by setting (t + -10) equal to 15.491933385 and -15.491933385.Subproblem 1
t + -10 = 15.491933385 Simplifying t + -10 = 15.491933385 Reorder the terms: -10 + t = 15.491933385 Solving -10 + t = 15.491933385 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 15.491933385 + 10 Combine like terms: -10 + 10 = 0 0 + t = 15.491933385 + 10 t = 15.491933385 + 10 Combine like terms: 15.491933385 + 10 = 25.491933385 t = 25.491933385 Simplifying t = 25.491933385Subproblem 2
t + -10 = -15.491933385 Simplifying t + -10 = -15.491933385 Reorder the terms: -10 + t = -15.491933385 Solving -10 + t = -15.491933385 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -15.491933385 + 10 Combine like terms: -10 + 10 = 0 0 + t = -15.491933385 + 10 t = -15.491933385 + 10 Combine like terms: -15.491933385 + 10 = -5.491933385 t = -5.491933385 Simplifying t = -5.491933385Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.491933385, -5.491933385}
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