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Simplifying 0 = -4.9t2 + 8t + 120 Reorder the terms: 0 = 120 + 8t + -4.9t2 Solving 0 = 120 + 8t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -120 = -120 -120 + -8t + 4.9t2 = 120 + 8t + -4.9t2 + -120 + -8t + 4.9t2 Reorder the terms: -120 + -8t + 4.9t2 = 120 + -120 + 8t + -8t + -4.9t2 + 4.9t2 Combine like terms: 120 + -120 = 0 -120 + -8t + 4.9t2 = 0 + 8t + -8t + -4.9t2 + 4.9t2 -120 + -8t + 4.9t2 = 8t + -8t + -4.9t2 + 4.9t2 Combine like terms: 8t + -8t = 0 -120 + -8t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -120 + -8t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -120 + -8t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -24.48979592 + -1.632653061t + t2 = 0 Move the constant term to the right: Add '24.48979592' to each side of the equation. -24.48979592 + -1.632653061t + 24.48979592 + t2 = 0 + 24.48979592 Reorder the terms: -24.48979592 + 24.48979592 + -1.632653061t + t2 = 0 + 24.48979592 Combine like terms: -24.48979592 + 24.48979592 = 0.00000000 0.00000000 + -1.632653061t + t2 = 0 + 24.48979592 -1.632653061t + t2 = 0 + 24.48979592 Combine like terms: 0 + 24.48979592 = 24.48979592 -1.632653061t + t2 = 24.48979592 The t term is -1.632653061t. Take half its coefficient (-0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. -1.632653061t + 0.6663890044 + t2 = 24.48979592 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061t + t2 = 24.48979592 + 0.6663890044 Combine like terms: 24.48979592 + 0.6663890044 = 25.1561849244 0.6663890044 + -1.632653061t + t2 = 25.1561849244 Factor a perfect square on the left side: (t + -0.8163265305)(t + -0.8163265305) = 25.1561849244 Calculate the square root of the right side: 5.015594175 Break this problem into two subproblems by setting (t + -0.8163265305) equal to 5.015594175 and -5.015594175.Subproblem 1
t + -0.8163265305 = 5.015594175 Simplifying t + -0.8163265305 = 5.015594175 Reorder the terms: -0.8163265305 + t = 5.015594175 Solving -0.8163265305 + t = 5.015594175 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = 5.015594175 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = 5.015594175 + 0.8163265305 t = 5.015594175 + 0.8163265305 Combine like terms: 5.015594175 + 0.8163265305 = 5.8319207055 t = 5.8319207055 Simplifying t = 5.8319207055Subproblem 2
t + -0.8163265305 = -5.015594175 Simplifying t + -0.8163265305 = -5.015594175 Reorder the terms: -0.8163265305 + t = -5.015594175 Solving -0.8163265305 + t = -5.015594175 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = -5.015594175 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = -5.015594175 + 0.8163265305 t = -5.015594175 + 0.8163265305 Combine like terms: -5.015594175 + 0.8163265305 = -4.1992676445 t = -4.1992676445 Simplifying t = -4.1992676445Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.8319207055, -4.1992676445}
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