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Simplifying 17.5 = 20t + -2.5t2 Solving 17.5 = 20t + -2.5t2 Solving for variable 't'. Reorder the terms: 17.5 + -20t + 2.5t2 = 20t + -20t + -2.5t2 + 2.5t2 Combine like terms: 20t + -20t = 0 17.5 + -20t + 2.5t2 = 0 + -2.5t2 + 2.5t2 17.5 + -20t + 2.5t2 = -2.5t2 + 2.5t2 Combine like terms: -2.5t2 + 2.5t2 = 0.0 17.5 + -20t + 2.5t2 = 0.0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 7 + -8t + t2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -8t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -8t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8t + t2 = 0 + -7 -8t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -8t + t2 = -7 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -7 + 16 Reorder the terms: 16 + -8t + t2 = -7 + 16 Combine like terms: -7 + 16 = 9 16 + -8t + t2 = 9 Factor a perfect square on the left side: (t + -4)(t + -4) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (t + -4) equal to 3 and -3.Subproblem 1
t + -4 = 3 Simplifying t + -4 = 3 Reorder the terms: -4 + t = 3 Solving -4 + t = 3 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3 + 4 t = 3 + 4 Combine like terms: 3 + 4 = 7 t = 7 Simplifying t = 7Subproblem 2
t + -4 = -3 Simplifying t + -4 = -3 Reorder the terms: -4 + t = -3 Solving -4 + t = -3 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3 + 4 t = -3 + 4 Combine like terms: -3 + 4 = 1 t = 1 Simplifying t = 1Solution
The solution to the problem is based on the solutions from the subproblems. t = {7, 1}
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