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Simplifying 99t + -5.5t2 = 308 Solving 99t + -5.5t2 = 308 Solving for variable 't'. Reorder the terms: -308 + 99t + -5.5t2 = 308 + -308 Combine like terms: 308 + -308 = 0 -308 + 99t + -5.5t2 = 0 Begin completing the square. Divide all terms by -5.5 the coefficient of the squared term: Divide each side by '-5.5'. 56 + -18t + t2 = 0 Move the constant term to the right: Add '-56' to each side of the equation. 56 + -18t + -56 + t2 = 0 + -56 Reorder the terms: 56 + -56 + -18t + t2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -18t + t2 = 0 + -56 -18t + t2 = 0 + -56 Combine like terms: 0 + -56 = -56 -18t + t2 = -56 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = -56 + 81 Reorder the terms: 81 + -18t + t2 = -56 + 81 Combine like terms: -56 + 81 = 25 81 + -18t + t2 = 25 Factor a perfect square on the left side: (t + -9)(t + -9) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (t + -9) equal to 5 and -5.Subproblem 1
t + -9 = 5 Simplifying t + -9 = 5 Reorder the terms: -9 + t = 5 Solving -9 + t = 5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 5 + 9 Combine like terms: -9 + 9 = 0 0 + t = 5 + 9 t = 5 + 9 Combine like terms: 5 + 9 = 14 t = 14 Simplifying t = 14Subproblem 2
t + -9 = -5 Simplifying t + -9 = -5 Reorder the terms: -9 + t = -5 Solving -9 + t = -5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -5 + 9 Combine like terms: -9 + 9 = 0 0 + t = -5 + 9 t = -5 + 9 Combine like terms: -5 + 9 = 4 t = 4 Simplifying t = 4Solution
The solution to the problem is based on the solutions from the subproblems. t = {14, 4}
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