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Simplifying 96 = 96t + -17t2 Solving 96 = 96t + -17t2 Solving for variable 't'. Reorder the terms: 96 + -96t + 17t2 = 96t + -96t + -17t2 + 17t2 Combine like terms: 96t + -96t = 0 96 + -96t + 17t2 = 0 + -17t2 + 17t2 96 + -96t + 17t2 = -17t2 + 17t2 Combine like terms: -17t2 + 17t2 = 0 96 + -96t + 17t2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 5.647058824 + -5.647058824t + t2 = 0 Move the constant term to the right: Add '-5.647058824' to each side of the equation. 5.647058824 + -5.647058824t + -5.647058824 + t2 = 0 + -5.647058824 Reorder the terms: 5.647058824 + -5.647058824 + -5.647058824t + t2 = 0 + -5.647058824 Combine like terms: 5.647058824 + -5.647058824 = 0.000000000 0.000000000 + -5.647058824t + t2 = 0 + -5.647058824 -5.647058824t + t2 = 0 + -5.647058824 Combine like terms: 0 + -5.647058824 = -5.647058824 -5.647058824t + t2 = -5.647058824 The t term is -5.647058824t. Take half its coefficient (-2.823529412). Square it (7.972318340) and add it to both sides. Add '7.972318340' to each side of the equation. -5.647058824t + 7.972318340 + t2 = -5.647058824 + 7.972318340 Reorder the terms: 7.972318340 + -5.647058824t + t2 = -5.647058824 + 7.972318340 Combine like terms: -5.647058824 + 7.972318340 = 2.325259516 7.972318340 + -5.647058824t + t2 = 2.325259516 Factor a perfect square on the left side: (t + -2.823529412)(t + -2.823529412) = 2.325259516 Calculate the square root of the right side: 1.524880164 Break this problem into two subproblems by setting (t + -2.823529412) equal to 1.524880164 and -1.524880164.Subproblem 1
t + -2.823529412 = 1.524880164 Simplifying t + -2.823529412 = 1.524880164 Reorder the terms: -2.823529412 + t = 1.524880164 Solving -2.823529412 + t = 1.524880164 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.823529412' to each side of the equation. -2.823529412 + 2.823529412 + t = 1.524880164 + 2.823529412 Combine like terms: -2.823529412 + 2.823529412 = 0.000000000 0.000000000 + t = 1.524880164 + 2.823529412 t = 1.524880164 + 2.823529412 Combine like terms: 1.524880164 + 2.823529412 = 4.348409576 t = 4.348409576 Simplifying t = 4.348409576Subproblem 2
t + -2.823529412 = -1.524880164 Simplifying t + -2.823529412 = -1.524880164 Reorder the terms: -2.823529412 + t = -1.524880164 Solving -2.823529412 + t = -1.524880164 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.823529412' to each side of the equation. -2.823529412 + 2.823529412 + t = -1.524880164 + 2.823529412 Combine like terms: -2.823529412 + 2.823529412 = 0.000000000 0.000000000 + t = -1.524880164 + 2.823529412 t = -1.524880164 + 2.823529412 Combine like terms: -1.524880164 + 2.823529412 = 1.298649248 t = 1.298649248 Simplifying t = 1.298649248Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.348409576, 1.298649248}
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