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Simplifying 45.1 = 15t + 0.5t2 Solving 45.1 = 15t + 0.5t2 Solving for variable 't'. Reorder the terms: 45.1 + -15t + -0.5t2 = 15t + -15t + 0.5t2 + -0.5t2 Combine like terms: 15t + -15t = 0 45.1 + -15t + -0.5t2 = 0 + 0.5t2 + -0.5t2 45.1 + -15t + -0.5t2 = 0.5t2 + -0.5t2 Combine like terms: 0.5t2 + -0.5t2 = 0.0 45.1 + -15t + -0.5t2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -90.2 + 30t + t2 = 0 Move the constant term to the right: Add '90.2' to each side of the equation. -90.2 + 30t + 90.2 + t2 = 0 + 90.2 Reorder the terms: -90.2 + 90.2 + 30t + t2 = 0 + 90.2 Combine like terms: -90.2 + 90.2 = 0.0 0.0 + 30t + t2 = 0 + 90.2 30t + t2 = 0 + 90.2 Combine like terms: 0 + 90.2 = 90.2 30t + t2 = 90.2 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 = 90.2 + 225 Reorder the terms: 225 + 30t + t2 = 90.2 + 225 Combine like terms: 90.2 + 225 = 315.2 225 + 30t + t2 = 315.2 Factor a perfect square on the left side: (t + 15)(t + 15) = 315.2 Calculate the square root of the right side: 17.753872817 Break this problem into two subproblems by setting (t + 15) equal to 17.753872817 and -17.753872817.Subproblem 1
t + 15 = 17.753872817 Simplifying t + 15 = 17.753872817 Reorder the terms: 15 + t = 17.753872817 Solving 15 + t = 17.753872817 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 = 17.753872817 + -15 Combine like terms: 15 + -15 = 0 0 + t = 17.753872817 + -15 t = 17.753872817 + -15 Combine like terms: 17.753872817 + -15 = 2.753872817 t = 2.753872817 Simplifying t = 2.753872817Subproblem 2
t + 15 = -17.753872817 Simplifying t + 15 = -17.753872817 Reorder the terms: 15 + t = -17.753872817 Solving 15 + t = -17.753872817 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 = -17.753872817 + -15 Combine like terms: 15 + -15 = 0 0 + t = -17.753872817 + -15 t = -17.753872817 + -15 Combine like terms: -17.753872817 + -15 = -32.753872817 t = -32.753872817 Simplifying t = -32.753872817Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.753872817, -32.753872817}
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