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Simplifying t = 45 + -5t + -5t2 Solving t = 45 + -5t + -5t2 Solving for variable 't'. Reorder the terms: -45 + t + 5t + 5t2 = 45 + -5t + -5t2 + -45 + 5t + 5t2 Combine like terms: t + 5t = 6t -45 + 6t + 5t2 = 45 + -5t + -5t2 + -45 + 5t + 5t2 Reorder the terms: -45 + 6t + 5t2 = 45 + -45 + -5t + 5t + -5t2 + 5t2 Combine like terms: 45 + -45 = 0 -45 + 6t + 5t2 = 0 + -5t + 5t + -5t2 + 5t2 -45 + 6t + 5t2 = -5t + 5t + -5t2 + 5t2 Combine like terms: -5t + 5t = 0 -45 + 6t + 5t2 = 0 + -5t2 + 5t2 -45 + 6t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -45 + 6t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9 + 1.2t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 1.2t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + 1.2t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1.2t + t2 = 0 + 9 1.2t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 1.2t + t2 = 9 The t term is 1.2t. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2t + 0.36 + t2 = 9 + 0.36 Reorder the terms: 0.36 + 1.2t + t2 = 9 + 0.36 Combine like terms: 9 + 0.36 = 9.36 0.36 + 1.2t + t2 = 9.36 Factor a perfect square on the left side: (t + 0.6)(t + 0.6) = 9.36 Calculate the square root of the right side: 3.059411708 Break this problem into two subproblems by setting (t + 0.6) equal to 3.059411708 and -3.059411708.Subproblem 1
t + 0.6 = 3.059411708 Simplifying t + 0.6 = 3.059411708 Reorder the terms: 0.6 + t = 3.059411708 Solving 0.6 + t = 3.059411708 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = 3.059411708 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = 3.059411708 + -0.6 t = 3.059411708 + -0.6 Combine like terms: 3.059411708 + -0.6 = 2.459411708 t = 2.459411708 Simplifying t = 2.459411708Subproblem 2
t + 0.6 = -3.059411708 Simplifying t + 0.6 = -3.059411708 Reorder the terms: 0.6 + t = -3.059411708 Solving 0.6 + t = -3.059411708 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = -3.059411708 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = -3.059411708 + -0.6 t = -3.059411708 + -0.6 Combine like terms: -3.059411708 + -0.6 = -3.659411708 t = -3.659411708 Simplifying t = -3.659411708Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.459411708, -3.659411708}
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