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Simplifying 12 = -4.9t2 + 120t Reorder the terms: 12 = 120t + -4.9t2 Solving 12 = 120t + -4.9t2 Solving for variable 't'. Reorder the terms: 12 + -120t + 4.9t2 = 120t + -120t + -4.9t2 + 4.9t2 Combine like terms: 120t + -120t = 0 12 + -120t + 4.9t2 = 0 + -4.9t2 + 4.9t2 12 + -120t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 12 + -120t + 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'. 2.448979592 + -24.48979592t + t2 = 0 Move the constant term to the right: Add '-2.448979592' to each side of the equation. 2.448979592 + -24.48979592t + -2.448979592 + t2 = 0 + -2.448979592 Reorder the terms: 2.448979592 + -2.448979592 + -24.48979592t + t2 = 0 + -2.448979592 Combine like terms: 2.448979592 + -2.448979592 = 0.000000000 0.000000000 + -24.48979592t + t2 = 0 + -2.448979592 -24.48979592t + t2 = 0 + -2.448979592 Combine like terms: 0 + -2.448979592 = -2.448979592 -24.48979592t + t2 = -2.448979592 The t term is -24.48979592t. Take half its coefficient (-12.24489796). Square it (149.9375261) and add it to both sides. Add '149.9375261' to each side of the equation. -24.48979592t + 149.9375261 + t2 = -2.448979592 + 149.9375261 Reorder the terms: 149.9375261 + -24.48979592t + t2 = -2.448979592 + 149.9375261 Combine like terms: -2.448979592 + 149.9375261 = 147.488546508 149.9375261 + -24.48979592t + t2 = 147.488546508 Factor a perfect square on the left side: (t + -12.24489796)(t + -12.24489796) = 147.488546508 Calculate the square root of the right side: 12.14448626 Break this problem into two subproblems by setting (t + -12.24489796) equal to 12.14448626 and -12.14448626.Subproblem 1
t + -12.24489796 = 12.14448626 Simplifying t + -12.24489796 = 12.14448626 Reorder the terms: -12.24489796 + t = 12.14448626 Solving -12.24489796 + t = 12.14448626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.24489796' to each side of the equation. -12.24489796 + 12.24489796 + t = 12.14448626 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + t = 12.14448626 + 12.24489796 t = 12.14448626 + 12.24489796 Combine like terms: 12.14448626 + 12.24489796 = 24.38938422 t = 24.38938422 Simplifying t = 24.38938422Subproblem 2
t + -12.24489796 = -12.14448626 Simplifying t + -12.24489796 = -12.14448626 Reorder the terms: -12.24489796 + t = -12.14448626 Solving -12.24489796 + t = -12.14448626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.24489796' to each side of the equation. -12.24489796 + 12.24489796 + t = -12.14448626 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + t = -12.14448626 + 12.24489796 t = -12.14448626 + 12.24489796 Combine like terms: -12.14448626 + 12.24489796 = 0.1004117 t = 0.1004117 Simplifying t = 0.1004117Solution
The solution to the problem is based on the solutions from the subproblems. t = {24.38938422, 0.1004117}
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