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Simplifying 0 = 6 + 96t + -17t2 Solving 0 = 6 + 96t + -17t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -96t + 17t2 = 6 + 96t + -17t2 + -6 + -96t + 17t2 Reorder the terms: -6 + -96t + 17t2 = 6 + -6 + 96t + -96t + -17t2 + 17t2 Combine like terms: 6 + -6 = 0 -6 + -96t + 17t2 = 0 + 96t + -96t + -17t2 + 17t2 -6 + -96t + 17t2 = 96t + -96t + -17t2 + 17t2 Combine like terms: 96t + -96t = 0 -6 + -96t + 17t2 = 0 + -17t2 + 17t2 -6 + -96t + 17t2 = -17t2 + 17t2 Combine like terms: -17t2 + 17t2 = 0 -6 + -96t + 17t2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.3529411765 + -5.647058824t + t2 = 0 Move the constant term to the right: Add '0.3529411765' to each side of the equation. -0.3529411765 + -5.647058824t + 0.3529411765 + t2 = 0 + 0.3529411765 Reorder the terms: -0.3529411765 + 0.3529411765 + -5.647058824t + t2 = 0 + 0.3529411765 Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000 0.0000000000 + -5.647058824t + t2 = 0 + 0.3529411765 -5.647058824t + t2 = 0 + 0.3529411765 Combine like terms: 0 + 0.3529411765 = 0.3529411765 -5.647058824t + t2 = 0.3529411765 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 = 0.3529411765 + 7.972318340 Reorder the terms: 7.972318340 + -5.647058824t + t2 = 0.3529411765 + 7.972318340 Combine like terms: 0.3529411765 + 7.972318340 = 8.3252595165 7.972318340 + -5.647058824t + t2 = 8.3252595165 Factor a perfect square on the left side: (t + -2.823529412)(t + -2.823529412) = 8.3252595165 Calculate the square root of the right side: 2.885352581 Break this problem into two subproblems by setting (t + -2.823529412) equal to 2.885352581 and -2.885352581.Subproblem 1
t + -2.823529412 = 2.885352581 Simplifying t + -2.823529412 = 2.885352581 Reorder the terms: -2.823529412 + t = 2.885352581 Solving -2.823529412 + t = 2.885352581 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 = 2.885352581 + 2.823529412 Combine like terms: -2.823529412 + 2.823529412 = 0.000000000 0.000000000 + t = 2.885352581 + 2.823529412 t = 2.885352581 + 2.823529412 Combine like terms: 2.885352581 + 2.823529412 = 5.708881993 t = 5.708881993 Simplifying t = 5.708881993Subproblem 2
t + -2.823529412 = -2.885352581 Simplifying t + -2.823529412 = -2.885352581 Reorder the terms: -2.823529412 + t = -2.885352581 Solving -2.823529412 + t = -2.885352581 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 = -2.885352581 + 2.823529412 Combine like terms: -2.823529412 + 2.823529412 = 0.000000000 0.000000000 + t = -2.885352581 + 2.823529412 t = -2.885352581 + 2.823529412 Combine like terms: -2.885352581 + 2.823529412 = -0.061823169 t = -0.061823169 Simplifying t = -0.061823169Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.708881993, -0.061823169}
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