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Simplifying 16t2 + -183t + 95 = 0 Reorder the terms: 95 + -183t + 16t2 = 0 Solving 95 + -183t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.9375 + -11.4375t + t2 = 0 Move the constant term to the right: Add '-5.9375' to each side of the equation. 5.9375 + -11.4375t + -5.9375 + t2 = 0 + -5.9375 Reorder the terms: 5.9375 + -5.9375 + -11.4375t + t2 = 0 + -5.9375 Combine like terms: 5.9375 + -5.9375 = 0.0000 0.0000 + -11.4375t + t2 = 0 + -5.9375 -11.4375t + t2 = 0 + -5.9375 Combine like terms: 0 + -5.9375 = -5.9375 -11.4375t + t2 = -5.9375 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 = -5.9375 + 32.70410156 Reorder the terms: 32.70410156 + -11.4375t + t2 = -5.9375 + 32.70410156 Combine like terms: -5.9375 + 32.70410156 = 26.76660156 32.70410156 + -11.4375t + t2 = 26.76660156 Factor a perfect square on the left side: (t + -5.71875)(t + -5.71875) = 26.76660156 Calculate the square root of the right side: 5.173644901 Break this problem into two subproblems by setting (t + -5.71875) equal to 5.173644901 and -5.173644901.Subproblem 1
t + -5.71875 = 5.173644901 Simplifying t + -5.71875 = 5.173644901 Reorder the terms: -5.71875 + t = 5.173644901 Solving -5.71875 + t = 5.173644901 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 = 5.173644901 + 5.71875 Combine like terms: -5.71875 + 5.71875 = 0.00000 0.00000 + t = 5.173644901 + 5.71875 t = 5.173644901 + 5.71875 Combine like terms: 5.173644901 + 5.71875 = 10.892394901 t = 10.892394901 Simplifying t = 10.892394901Subproblem 2
t + -5.71875 = -5.173644901 Simplifying t + -5.71875 = -5.173644901 Reorder the terms: -5.71875 + t = -5.173644901 Solving -5.71875 + t = -5.173644901 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 = -5.173644901 + 5.71875 Combine like terms: -5.71875 + 5.71875 = 0.00000 0.00000 + t = -5.173644901 + 5.71875 t = -5.173644901 + 5.71875 Combine like terms: -5.173644901 + 5.71875 = 0.545105099 t = 0.545105099 Simplifying t = 0.545105099Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.892394901, 0.545105099}
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