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Simplifying 5 = -16t2 + 124t Reorder the terms: 5 = 124t + -16t2 Solving 5 = 124t + -16t2 Solving for variable 't'. Reorder the terms: 5 + -124t + 16t2 = 124t + -124t + -16t2 + 16t2 Combine like terms: 124t + -124t = 0 5 + -124t + 16t2 = 0 + -16t2 + 16t2 5 + -124t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 5 + -124t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + -7.75t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -7.75t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -7.75t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -7.75t + t2 = 0 + -0.3125 -7.75t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -7.75t + t2 = -0.3125 The t term is -7.75t. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75t + 15.015625 + t2 = -0.3125 + 15.015625 Reorder the terms: 15.015625 + -7.75t + t2 = -0.3125 + 15.015625 Combine like terms: -0.3125 + 15.015625 = 14.703125 15.015625 + -7.75t + t2 = 14.703125 Factor a perfect square on the left side: (t + -3.875)(t + -3.875) = 14.703125 Calculate the square root of the right side: 3.834465413 Break this problem into two subproblems by setting (t + -3.875) equal to 3.834465413 and -3.834465413.Subproblem 1
t + -3.875 = 3.834465413 Simplifying t + -3.875 = 3.834465413 Reorder the terms: -3.875 + t = 3.834465413 Solving -3.875 + t = 3.834465413 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + t = 3.834465413 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + t = 3.834465413 + 3.875 t = 3.834465413 + 3.875 Combine like terms: 3.834465413 + 3.875 = 7.709465413 t = 7.709465413 Simplifying t = 7.709465413Subproblem 2
t + -3.875 = -3.834465413 Simplifying t + -3.875 = -3.834465413 Reorder the terms: -3.875 + t = -3.834465413 Solving -3.875 + t = -3.834465413 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + t = -3.834465413 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + t = -3.834465413 + 3.875 t = -3.834465413 + 3.875 Combine like terms: -3.834465413 + 3.875 = 0.040534587 t = 0.040534587 Simplifying t = 0.040534587Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.709465413, 0.040534587}
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