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Simplifying 220 = -30t + (0.5)(9.8) * t2 Multiply 0.5 * 9.8 220 = -30t + 4.9t2 Solving 220 = -30t + 4.9t2 Solving for variable 't'. Reorder the terms: 220 + 30t + -4.9t2 = -30t + 30t + 4.9t2 + -4.9t2 Combine like terms: -30t + 30t = 0 220 + 30t + -4.9t2 = 0 + 4.9t2 + -4.9t2 220 + 30t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 220 + 30t + -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'. -44.89795918 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '44.89795918' to each side of the equation. -44.89795918 + -6.12244898t + 44.89795918 + t2 = 0 + 44.89795918 Reorder the terms: -44.89795918 + 44.89795918 + -6.12244898t + t2 = 0 + 44.89795918 Combine like terms: -44.89795918 + 44.89795918 = 0.00000000 0.00000000 + -6.12244898t + t2 = 0 + 44.89795918 -6.12244898t + t2 = 0 + 44.89795918 Combine like terms: 0 + 44.89795918 = 44.89795918 -6.12244898t + t2 = 44.89795918 The t term is -6.12244898t. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898t + 9.371095378 + t2 = 44.89795918 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = 44.89795918 + 9.371095378 Combine like terms: 44.89795918 + 9.371095378 = 54.269054558 9.371095378 + -6.12244898t + t2 = 54.269054558 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 54.269054558 Calculate the square root of the right side: 7.366753325 Break this problem into two subproblems by setting (t + -3.06122449) equal to 7.366753325 and -7.366753325.Subproblem 1
t + -3.06122449 = 7.366753325 Simplifying t + -3.06122449 = 7.366753325 Reorder the terms: -3.06122449 + t = 7.366753325 Solving -3.06122449 + t = 7.366753325 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = 7.366753325 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 7.366753325 + 3.06122449 t = 7.366753325 + 3.06122449 Combine like terms: 7.366753325 + 3.06122449 = 10.427977815 t = 10.427977815 Simplifying t = 10.427977815Subproblem 2
t + -3.06122449 = -7.366753325 Simplifying t + -3.06122449 = -7.366753325 Reorder the terms: -3.06122449 + t = -7.366753325 Solving -3.06122449 + t = -7.366753325 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = -7.366753325 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -7.366753325 + 3.06122449 t = -7.366753325 + 3.06122449 Combine like terms: -7.366753325 + 3.06122449 = -4.305528835 t = -4.305528835 Simplifying t = -4.305528835Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.427977815, -4.305528835}
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