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Simplifying 10 = -0.50t2 + 10.5t Reorder the terms: 10 = 10.5t + -0.50t2 Solving 10 = 10.5t + -0.50t2 Solving for variable 't'. Reorder the terms: 10 + -10.5t + 0.50t2 = 10.5t + -10.5t + -0.50t2 + 0.50t2 Combine like terms: 10.5t + -10.5t = 0.0 10 + -10.5t + 0.50t2 = 0.0 + -0.50t2 + 0.50t2 10 + -10.5t + 0.50t2 = -0.50t2 + 0.50t2 Combine like terms: -0.50t2 + 0.50t2 = 0.00 10 + -10.5t + 0.50t2 = 0.00 Begin completing the square. Divide all terms by 0.50 the coefficient of the squared term: Divide each side by '0.50'. 20 + -21t + t2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -21t + -20 + t2 = 0 + -20 Reorder the terms: 20 + -20 + -21t + t2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -21t + t2 = 0 + -20 -21t + t2 = 0 + -20 Combine like terms: 0 + -20 = -20 -21t + t2 = -20 The t term is -21t. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21t + 110.25 + t2 = -20 + 110.25 Reorder the terms: 110.25 + -21t + t2 = -20 + 110.25 Combine like terms: -20 + 110.25 = 90.25 110.25 + -21t + t2 = 90.25 Factor a perfect square on the left side: (t + -10.5)(t + -10.5) = 90.25 Calculate the square root of the right side: 9.5 Break this problem into two subproblems by setting (t + -10.5) equal to 9.5 and -9.5.Subproblem 1
t + -10.5 = 9.5 Simplifying t + -10.5 = 9.5 Reorder the terms: -10.5 + t = 9.5 Solving -10.5 + t = 9.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + t = 9.5 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + t = 9.5 + 10.5 t = 9.5 + 10.5 Combine like terms: 9.5 + 10.5 = 20 t = 20 Simplifying t = 20Subproblem 2
t + -10.5 = -9.5 Simplifying t + -10.5 = -9.5 Reorder the terms: -10.5 + t = -9.5 Solving -10.5 + t = -9.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + t = -9.5 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + t = -9.5 + 10.5 t = -9.5 + 10.5 Combine like terms: -9.5 + 10.5 = 1 t = 1 Simplifying t = 1Solution
The solution to the problem is based on the solutions from the subproblems. t = {20, 1}
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