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Simplifying -27.9 = 14.4t + 0.5(-9.8) * t2 Multiply 0.5 * -9.8 -27.9 = 14.4t + -4.9t2 Solving -27.9 = 14.4t + -4.9t2 Solving for variable 't'. Reorder the terms: -27.9 + -14.4t + 4.9t2 = 14.4t + -14.4t + -4.9t2 + 4.9t2 Combine like terms: 14.4t + -14.4t = 0.0 -27.9 + -14.4t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -27.9 + -14.4t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -27.9 + -14.4t + 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'. -5.693877551 + -2.93877551t + t2 = 0 Move the constant term to the right: Add '5.693877551' to each side of the equation. -5.693877551 + -2.93877551t + 5.693877551 + t2 = 0 + 5.693877551 Reorder the terms: -5.693877551 + 5.693877551 + -2.93877551t + t2 = 0 + 5.693877551 Combine like terms: -5.693877551 + 5.693877551 = 0.000000000 0.000000000 + -2.93877551t + t2 = 0 + 5.693877551 -2.93877551t + t2 = 0 + 5.693877551 Combine like terms: 0 + 5.693877551 = 5.693877551 -2.93877551t + t2 = 5.693877551 The t term is -2.93877551t. Take half its coefficient (-1.469387755). Square it (2.159100375) and add it to both sides. Add '2.159100375' to each side of the equation. -2.93877551t + 2.159100375 + t2 = 5.693877551 + 2.159100375 Reorder the terms: 2.159100375 + -2.93877551t + t2 = 5.693877551 + 2.159100375 Combine like terms: 5.693877551 + 2.159100375 = 7.852977926 2.159100375 + -2.93877551t + t2 = 7.852977926 Factor a perfect square on the left side: (t + -1.469387755)(t + -1.469387755) = 7.852977926 Calculate the square root of the right side: 2.802316529 Break this problem into two subproblems by setting (t + -1.469387755) equal to 2.802316529 and -2.802316529.Subproblem 1
t + -1.469387755 = 2.802316529 Simplifying t + -1.469387755 = 2.802316529 Reorder the terms: -1.469387755 + t = 2.802316529 Solving -1.469387755 + t = 2.802316529 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.469387755' to each side of the equation. -1.469387755 + 1.469387755 + t = 2.802316529 + 1.469387755 Combine like terms: -1.469387755 + 1.469387755 = 0.000000000 0.000000000 + t = 2.802316529 + 1.469387755 t = 2.802316529 + 1.469387755 Combine like terms: 2.802316529 + 1.469387755 = 4.271704284 t = 4.271704284 Simplifying t = 4.271704284Subproblem 2
t + -1.469387755 = -2.802316529 Simplifying t + -1.469387755 = -2.802316529 Reorder the terms: -1.469387755 + t = -2.802316529 Solving -1.469387755 + t = -2.802316529 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.469387755' to each side of the equation. -1.469387755 + 1.469387755 + t = -2.802316529 + 1.469387755 Combine like terms: -1.469387755 + 1.469387755 = 0.000000000 0.000000000 + t = -2.802316529 + 1.469387755 t = -2.802316529 + 1.469387755 Combine like terms: -2.802316529 + 1.469387755 = -1.332928774 t = -1.332928774 Simplifying t = -1.332928774Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.271704284, -1.332928774}
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