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Simplifying 0 = 43 + -4t + -5t2 Solving 0 = 43 + -4t + -5t2 Solving for variable 't'. Combine like terms: 0 + -43 = -43 -43 + 4t + 5t2 = 43 + -4t + -5t2 + -43 + 4t + 5t2 Reorder the terms: -43 + 4t + 5t2 = 43 + -43 + -4t + 4t + -5t2 + 5t2 Combine like terms: 43 + -43 = 0 -43 + 4t + 5t2 = 0 + -4t + 4t + -5t2 + 5t2 -43 + 4t + 5t2 = -4t + 4t + -5t2 + 5t2 Combine like terms: -4t + 4t = 0 -43 + 4t + 5t2 = 0 + -5t2 + 5t2 -43 + 4t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -43 + 4t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.6 + 0.8t + t2 = 0 Move the constant term to the right: Add '8.6' to each side of the equation. -8.6 + 0.8t + 8.6 + t2 = 0 + 8.6 Reorder the terms: -8.6 + 8.6 + 0.8t + t2 = 0 + 8.6 Combine like terms: -8.6 + 8.6 = 0.0 0.0 + 0.8t + t2 = 0 + 8.6 0.8t + t2 = 0 + 8.6 Combine like terms: 0 + 8.6 = 8.6 0.8t + t2 = 8.6 The t term is 0.8t. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8t + 0.16 + t2 = 8.6 + 0.16 Reorder the terms: 0.16 + 0.8t + t2 = 8.6 + 0.16 Combine like terms: 8.6 + 0.16 = 8.76 0.16 + 0.8t + t2 = 8.76 Factor a perfect square on the left side: (t + 0.4)(t + 0.4) = 8.76 Calculate the square root of the right side: 2.959729717 Break this problem into two subproblems by setting (t + 0.4) equal to 2.959729717 and -2.959729717.Subproblem 1
t + 0.4 = 2.959729717 Simplifying t + 0.4 = 2.959729717 Reorder the terms: 0.4 + t = 2.959729717 Solving 0.4 + t = 2.959729717 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + t = 2.959729717 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + t = 2.959729717 + -0.4 t = 2.959729717 + -0.4 Combine like terms: 2.959729717 + -0.4 = 2.559729717 t = 2.559729717 Simplifying t = 2.559729717Subproblem 2
t + 0.4 = -2.959729717 Simplifying t + 0.4 = -2.959729717 Reorder the terms: 0.4 + t = -2.959729717 Solving 0.4 + t = -2.959729717 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + t = -2.959729717 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + t = -2.959729717 + -0.4 t = -2.959729717 + -0.4 Combine like terms: -2.959729717 + -0.4 = -3.359729717 t = -3.359729717 Simplifying t = -3.359729717Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.559729717, -3.359729717}
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