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Simplifying 97 = 215t + -16t2 Solving 97 = 215t + -16t2 Solving for variable 't'. Reorder the terms: 97 + -215t + 16t2 = 215t + -215t + -16t2 + 16t2 Combine like terms: 215t + -215t = 0 97 + -215t + 16t2 = 0 + -16t2 + 16t2 97 + -215t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 97 + -215t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 6.0625 + -13.4375t + t2 = 0 Move the constant term to the right: Add '-6.0625' to each side of the equation. 6.0625 + -13.4375t + -6.0625 + t2 = 0 + -6.0625 Reorder the terms: 6.0625 + -6.0625 + -13.4375t + t2 = 0 + -6.0625 Combine like terms: 6.0625 + -6.0625 = 0.0000 0.0000 + -13.4375t + t2 = 0 + -6.0625 -13.4375t + t2 = 0 + -6.0625 Combine like terms: 0 + -6.0625 = -6.0625 -13.4375t + t2 = -6.0625 The t term is -13.4375t. Take half its coefficient (-6.71875). Square it (45.14160156) and add it to both sides. Add '45.14160156' to each side of the equation. -13.4375t + 45.14160156 + t2 = -6.0625 + 45.14160156 Reorder the terms: 45.14160156 + -13.4375t + t2 = -6.0625 + 45.14160156 Combine like terms: -6.0625 + 45.14160156 = 39.07910156 45.14160156 + -13.4375t + t2 = 39.07910156 Factor a perfect square on the left side: (t + -6.71875)(t + -6.71875) = 39.07910156 Calculate the square root of the right side: 6.251327984 Break this problem into two subproblems by setting (t + -6.71875) equal to 6.251327984 and -6.251327984.Subproblem 1
t + -6.71875 = 6.251327984 Simplifying t + -6.71875 = 6.251327984 Reorder the terms: -6.71875 + t = 6.251327984 Solving -6.71875 + t = 6.251327984 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + t = 6.251327984 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + t = 6.251327984 + 6.71875 t = 6.251327984 + 6.71875 Combine like terms: 6.251327984 + 6.71875 = 12.970077984 t = 12.970077984 Simplifying t = 12.970077984Subproblem 2
t + -6.71875 = -6.251327984 Simplifying t + -6.71875 = -6.251327984 Reorder the terms: -6.71875 + t = -6.251327984 Solving -6.71875 + t = -6.251327984 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + t = -6.251327984 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + t = -6.251327984 + 6.71875 t = -6.251327984 + 6.71875 Combine like terms: -6.251327984 + 6.71875 = 0.467422016 t = 0.467422016 Simplifying t = 0.467422016Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.970077984, 0.467422016}
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