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Simplifying 3.0 = 20(t) + (0.5)(9.81)(t2) Multiply 0.5 * 9.81 3.0 = 20t + 4.905t2 Solving 3.0 = 20t + 4.905t2 Solving for variable 't'. Reorder the terms: 3.0 + -20t + -4.905t2 = 20t + -20t + 4.905t2 + -4.905t2 Combine like terms: 20t + -20t = 0 3.0 + -20t + -4.905t2 = 0 + 4.905t2 + -4.905t2 3.0 + -20t + -4.905t2 = 4.905t2 + -4.905t2 Combine like terms: 4.905t2 + -4.905t2 = 0.000 3.0 + -20t + -4.905t2 = 0.000 Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -0.6116207951 + 4.077471967t + t2 = 0 Move the constant term to the right: Add '0.6116207951' to each side of the equation. -0.6116207951 + 4.077471967t + 0.6116207951 + t2 = 0 + 0.6116207951 Reorder the terms: -0.6116207951 + 0.6116207951 + 4.077471967t + t2 = 0 + 0.6116207951 Combine like terms: -0.6116207951 + 0.6116207951 = 0.0000000000 0.0000000000 + 4.077471967t + t2 = 0 + 0.6116207951 4.077471967t + t2 = 0 + 0.6116207951 Combine like terms: 0 + 0.6116207951 = 0.6116207951 4.077471967t + t2 = 0.6116207951 The t term is 4.077471967t. Take half its coefficient (2.038735984). Square it (4.156444412) and add it to both sides. Add '4.156444412' to each side of the equation. 4.077471967t + 4.156444412 + t2 = 0.6116207951 + 4.156444412 Reorder the terms: 4.156444412 + 4.077471967t + t2 = 0.6116207951 + 4.156444412 Combine like terms: 0.6116207951 + 4.156444412 = 4.7680652071 4.156444412 + 4.077471967t + t2 = 4.7680652071 Factor a perfect square on the left side: (t + 2.038735984)(t + 2.038735984) = 4.7680652071 Calculate the square root of the right side: 2.183589981 Break this problem into two subproblems by setting (t + 2.038735984) equal to 2.183589981 and -2.183589981.Subproblem 1
t + 2.038735984 = 2.183589981 Simplifying t + 2.038735984 = 2.183589981 Reorder the terms: 2.038735984 + t = 2.183589981 Solving 2.038735984 + t = 2.183589981 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.038735984' to each side of the equation. 2.038735984 + -2.038735984 + t = 2.183589981 + -2.038735984 Combine like terms: 2.038735984 + -2.038735984 = 0.000000000 0.000000000 + t = 2.183589981 + -2.038735984 t = 2.183589981 + -2.038735984 Combine like terms: 2.183589981 + -2.038735984 = 0.144853997 t = 0.144853997 Simplifying t = 0.144853997Subproblem 2
t + 2.038735984 = -2.183589981 Simplifying t + 2.038735984 = -2.183589981 Reorder the terms: 2.038735984 + t = -2.183589981 Solving 2.038735984 + t = -2.183589981 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.038735984' to each side of the equation. 2.038735984 + -2.038735984 + t = -2.183589981 + -2.038735984 Combine like terms: 2.038735984 + -2.038735984 = 0.000000000 0.000000000 + t = -2.183589981 + -2.038735984 t = -2.183589981 + -2.038735984 Combine like terms: -2.183589981 + -2.038735984 = -4.222325965 t = -4.222325965 Simplifying t = -4.222325965Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.144853997, -4.222325965}
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