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Simplifying 183 = 183t + -16t2 Solving 183 = 183t + -16t2 Solving for variable 't'. Reorder the terms: 183 + -183t + 16t2 = 183t + -183t + -16t2 + 16t2 Combine like terms: 183t + -183t = 0 183 + -183t + 16t2 = 0 + -16t2 + 16t2 183 + -183t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 183 + -183t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 11.4375 + -11.4375t + t2 = 0 Move the constant term to the right: Add '-11.4375' to each side of the equation. 11.4375 + -11.4375t + -11.4375 + t2 = 0 + -11.4375 Reorder the terms: 11.4375 + -11.4375 + -11.4375t + t2 = 0 + -11.4375 Combine like terms: 11.4375 + -11.4375 = 0.0000 0.0000 + -11.4375t + t2 = 0 + -11.4375 -11.4375t + t2 = 0 + -11.4375 Combine like terms: 0 + -11.4375 = -11.4375 -11.4375t + t2 = -11.4375 The t term is -11.4375t. Take half its coefficient (-5.71875). Square it (32.70410156) and add it to both sides. Add '32.70410156' to each side of the equation. -11.4375t + 32.70410156 + t2 = -11.4375 + 32.70410156 Reorder the terms: 32.70410156 + -11.4375t + t2 = -11.4375 + 32.70410156 Combine like terms: -11.4375 + 32.70410156 = 21.26660156 32.70410156 + -11.4375t + t2 = 21.26660156 Factor a perfect square on the left side: (t + -5.71875)(t + -5.71875) = 21.26660156 Calculate the square root of the right side: 4.611572569 Break this problem into two subproblems by setting (t + -5.71875) equal to 4.611572569 and -4.611572569.Subproblem 1
t + -5.71875 = 4.611572569 Simplifying t + -5.71875 = 4.611572569 Reorder the terms: -5.71875 + t = 4.611572569 Solving -5.71875 + t = 4.611572569 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.71875' to each side of the equation. -5.71875 + 5.71875 + t = 4.611572569 + 5.71875 Combine like terms: -5.71875 + 5.71875 = 0.00000 0.00000 + t = 4.611572569 + 5.71875 t = 4.611572569 + 5.71875 Combine like terms: 4.611572569 + 5.71875 = 10.330322569 t = 10.330322569 Simplifying t = 10.330322569Subproblem 2
t + -5.71875 = -4.611572569 Simplifying t + -5.71875 = -4.611572569 Reorder the terms: -5.71875 + t = -4.611572569 Solving -5.71875 + t = -4.611572569 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.71875' to each side of the equation. -5.71875 + 5.71875 + t = -4.611572569 + 5.71875 Combine like terms: -5.71875 + 5.71875 = 0.00000 0.00000 + t = -4.611572569 + 5.71875 t = -4.611572569 + 5.71875 Combine like terms: -4.611572569 + 5.71875 = 1.107177431 t = 1.107177431 Simplifying t = 1.107177431Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.330322569, 1.107177431}
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