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Simplifying 429.87 = -2.67t2 + 80.1t + 0 Reorder the terms: 429.87 = 0 + 80.1t + -2.67t2 Remove the zero: 429.87 = 80.1t + -2.67t2 Solving 429.87 = 80.1t + -2.67t2 Solving for variable 't'. Reorder the terms: 429.87 + -80.1t + 2.67t2 = 80.1t + -80.1t + -2.67t2 + 2.67t2 Combine like terms: 80.1t + -80.1t = 0.0 429.87 + -80.1t + 2.67t2 = 0.0 + -2.67t2 + 2.67t2 429.87 + -80.1t + 2.67t2 = -2.67t2 + 2.67t2 Combine like terms: -2.67t2 + 2.67t2 = 0.00 429.87 + -80.1t + 2.67t2 = 0.00 Begin completing the square. Divide all terms by 2.67 the coefficient of the squared term: Divide each side by '2.67'. 161 + -30t + t2 = 0 Move the constant term to the right: Add '-161' to each side of the equation. 161 + -30t + -161 + t2 = 0 + -161 Reorder the terms: 161 + -161 + -30t + t2 = 0 + -161 Combine like terms: 161 + -161 = 0 0 + -30t + t2 = 0 + -161 -30t + t2 = 0 + -161 Combine like terms: 0 + -161 = -161 -30t + t2 = -161 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = -161 + 225 Reorder the terms: 225 + -30t + t2 = -161 + 225 Combine like terms: -161 + 225 = 64 225 + -30t + t2 = 64 Factor a perfect square on the left side: (t + -15)(t + -15) = 64 Calculate the square root of the right side: 8 Break this problem into two subproblems by setting (t + -15) equal to 8 and -8.Subproblem 1
t + -15 = 8 Simplifying t + -15 = 8 Reorder the terms: -15 + t = 8 Solving -15 + t = 8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 8 + 15 Combine like terms: -15 + 15 = 0 0 + t = 8 + 15 t = 8 + 15 Combine like terms: 8 + 15 = 23 t = 23 Simplifying t = 23Subproblem 2
t + -15 = -8 Simplifying t + -15 = -8 Reorder the terms: -15 + t = -8 Solving -15 + t = -8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -8 + 15 Combine like terms: -15 + 15 = 0 0 + t = -8 + 15 t = -8 + 15 Combine like terms: -8 + 15 = 7 t = 7 Simplifying t = 7Solution
The solution to the problem is based on the solutions from the subproblems. t = {23, 7}
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