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Simplifying 19.2 = -0.8t2 + 8t Reorder the terms: 19.2 = 8t + -0.8t2 Solving 19.2 = 8t + -0.8t2 Solving for variable 't'. Reorder the terms: 19.2 + -8t + 0.8t2 = 8t + -8t + -0.8t2 + 0.8t2 Combine like terms: 8t + -8t = 0 19.2 + -8t + 0.8t2 = 0 + -0.8t2 + 0.8t2 19.2 + -8t + 0.8t2 = -0.8t2 + 0.8t2 Combine like terms: -0.8t2 + 0.8t2 = 0.0 19.2 + -8t + 0.8t2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 24 + -10t + t2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -10t + -24 + t2 = 0 + -24 Reorder the terms: 24 + -24 + -10t + t2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -10t + t2 = 0 + -24 -10t + t2 = 0 + -24 Combine like terms: 0 + -24 = -24 -10t + t2 = -24 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -24 + 25 Reorder the terms: 25 + -10t + t2 = -24 + 25 Combine like terms: -24 + 25 = 1 25 + -10t + t2 = 1 Factor a perfect square on the left side: (t + -5)(t + -5) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (t + -5) equal to 1 and -1.Subproblem 1
t + -5 = 1 Simplifying t + -5 = 1 Reorder the terms: -5 + t = 1 Solving -5 + t = 1 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 1 + 5 Combine like terms: -5 + 5 = 0 0 + t = 1 + 5 t = 1 + 5 Combine like terms: 1 + 5 = 6 t = 6 Simplifying t = 6Subproblem 2
t + -5 = -1 Simplifying t + -5 = -1 Reorder the terms: -5 + t = -1 Solving -5 + t = -1 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -1 + 5 Combine like terms: -5 + 5 = 0 0 + t = -1 + 5 t = -1 + 5 Combine like terms: -1 + 5 = 4 t = 4 Simplifying t = 4Solution
The solution to the problem is based on the solutions from the subproblems. t = {6, 4}
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