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Simplifying 0 = 105 + 63.19t + -0.5 * 9.81t2 Multiply -0.5 * 9.81 0 = 105 + 63.19t + -4.905t2 Solving 0 = 105 + 63.19t + -4.905t2 Solving for variable 't'. Combine like terms: 0 + -105 = -105 -105 + -63.19t + 4.905t2 = 105 + 63.19t + -4.905t2 + -105 + -63.19t + 4.905t2 Reorder the terms: -105 + -63.19t + 4.905t2 = 105 + -105 + 63.19t + -63.19t + -4.905t2 + 4.905t2 Combine like terms: 105 + -105 = 0 -105 + -63.19t + 4.905t2 = 0 + 63.19t + -63.19t + -4.905t2 + 4.905t2 -105 + -63.19t + 4.905t2 = 63.19t + -63.19t + -4.905t2 + 4.905t2 Combine like terms: 63.19t + -63.19t = 0.00 -105 + -63.19t + 4.905t2 = 0.00 + -4.905t2 + 4.905t2 -105 + -63.19t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 -105 + -63.19t + 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'. -21.40672783 + -12.88277268t + t2 = 0 Move the constant term to the right: Add '21.40672783' to each side of the equation. -21.40672783 + -12.88277268t + 21.40672783 + t2 = 0 + 21.40672783 Reorder the terms: -21.40672783 + 21.40672783 + -12.88277268t + t2 = 0 + 21.40672783 Combine like terms: -21.40672783 + 21.40672783 = 0.00000000 0.00000000 + -12.88277268t + t2 = 0 + 21.40672783 -12.88277268t + t2 = 0 + 21.40672783 Combine like terms: 0 + 21.40672783 = 21.40672783 -12.88277268t + t2 = 21.40672783 The t term is -12.88277268t. Take half its coefficient (-6.44138634). Square it (41.49145798) and add it to both sides. Add '41.49145798' to each side of the equation. -12.88277268t + 41.49145798 + t2 = 21.40672783 + 41.49145798 Reorder the terms: 41.49145798 + -12.88277268t + t2 = 21.40672783 + 41.49145798 Combine like terms: 21.40672783 + 41.49145798 = 62.89818581 41.49145798 + -12.88277268t + t2 = 62.89818581 Factor a perfect square on the left side: (t + -6.44138634)(t + -6.44138634) = 62.89818581 Calculate the square root of the right side: 7.930837649 Break this problem into two subproblems by setting (t + -6.44138634) equal to 7.930837649 and -7.930837649.Subproblem 1
t + -6.44138634 = 7.930837649 Simplifying t + -6.44138634 = 7.930837649 Reorder the terms: -6.44138634 + t = 7.930837649 Solving -6.44138634 + t = 7.930837649 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.44138634' to each side of the equation. -6.44138634 + 6.44138634 + t = 7.930837649 + 6.44138634 Combine like terms: -6.44138634 + 6.44138634 = 0.00000000 0.00000000 + t = 7.930837649 + 6.44138634 t = 7.930837649 + 6.44138634 Combine like terms: 7.930837649 + 6.44138634 = 14.372223989 t = 14.372223989 Simplifying t = 14.372223989Subproblem 2
t + -6.44138634 = -7.930837649 Simplifying t + -6.44138634 = -7.930837649 Reorder the terms: -6.44138634 + t = -7.930837649 Solving -6.44138634 + t = -7.930837649 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.44138634' to each side of the equation. -6.44138634 + 6.44138634 + t = -7.930837649 + 6.44138634 Combine like terms: -6.44138634 + 6.44138634 = 0.00000000 0.00000000 + t = -7.930837649 + 6.44138634 t = -7.930837649 + 6.44138634 Combine like terms: -7.930837649 + 6.44138634 = -1.489451309 t = -1.489451309 Simplifying t = -1.489451309Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.372223989, -1.489451309}
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