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Simplifying -4.9t2 + 92t + -141 = 0 Reorder the terms: -141 + 92t + -4.9t2 = 0 Solving -141 + 92t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 28.7755102 + -18.7755102t + t2 = 0 Move the constant term to the right: Add '-28.7755102' to each side of the equation. 28.7755102 + -18.7755102t + -28.7755102 + t2 = 0 + -28.7755102 Reorder the terms: 28.7755102 + -28.7755102 + -18.7755102t + t2 = 0 + -28.7755102 Combine like terms: 28.7755102 + -28.7755102 = 0.0000000 0.0000000 + -18.7755102t + t2 = 0 + -28.7755102 -18.7755102t + t2 = 0 + -28.7755102 Combine like terms: 0 + -28.7755102 = -28.7755102 -18.7755102t + t2 = -28.7755102 The t term is -18.7755102t. Take half its coefficient (-9.3877551). Square it (88.12994582) and add it to both sides. Add '88.12994582' to each side of the equation. -18.7755102t + 88.12994582 + t2 = -28.7755102 + 88.12994582 Reorder the terms: 88.12994582 + -18.7755102t + t2 = -28.7755102 + 88.12994582 Combine like terms: -28.7755102 + 88.12994582 = 59.35443562 88.12994582 + -18.7755102t + t2 = 59.35443562 Factor a perfect square on the left side: (t + -9.3877551)(t + -9.3877551) = 59.35443562 Calculate the square root of the right side: 7.704182995 Break this problem into two subproblems by setting (t + -9.3877551) equal to 7.704182995 and -7.704182995.Subproblem 1
t + -9.3877551 = 7.704182995 Simplifying t + -9.3877551 = 7.704182995 Reorder the terms: -9.3877551 + t = 7.704182995 Solving -9.3877551 + t = 7.704182995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.3877551' to each side of the equation. -9.3877551 + 9.3877551 + t = 7.704182995 + 9.3877551 Combine like terms: -9.3877551 + 9.3877551 = 0.0000000 0.0000000 + t = 7.704182995 + 9.3877551 t = 7.704182995 + 9.3877551 Combine like terms: 7.704182995 + 9.3877551 = 17.091938095 t = 17.091938095 Simplifying t = 17.091938095Subproblem 2
t + -9.3877551 = -7.704182995 Simplifying t + -9.3877551 = -7.704182995 Reorder the terms: -9.3877551 + t = -7.704182995 Solving -9.3877551 + t = -7.704182995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.3877551' to each side of the equation. -9.3877551 + 9.3877551 + t = -7.704182995 + 9.3877551 Combine like terms: -9.3877551 + 9.3877551 = 0.0000000 0.0000000 + t = -7.704182995 + 9.3877551 t = -7.704182995 + 9.3877551 Combine like terms: -7.704182995 + 9.3877551 = 1.683572105 t = 1.683572105 Simplifying t = 1.683572105Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.091938095, 1.683572105}
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