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Simplifying 5t2 + 8t + -20 = 0 Reorder the terms: -20 + 8t + 5t2 = 0 Solving -20 + 8t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 1.6t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.6t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 1.6t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.6t + t2 = 0 + 4 1.6t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.6t + t2 = 4 The t term is 1.6t. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6t + 0.64 + t2 = 4 + 0.64 Reorder the terms: 0.64 + 1.6t + t2 = 4 + 0.64 Combine like terms: 4 + 0.64 = 4.64 0.64 + 1.6t + t2 = 4.64 Factor a perfect square on the left side: (t + 0.8)(t + 0.8) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (t + 0.8) equal to 2.154065923 and -2.154065923.Subproblem 1
t + 0.8 = 2.154065923 Simplifying t + 0.8 = 2.154065923 Reorder the terms: 0.8 + t = 2.154065923 Solving 0.8 + t = 2.154065923 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = 2.154065923 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = 2.154065923 + -0.8 t = 2.154065923 + -0.8 Combine like terms: 2.154065923 + -0.8 = 1.354065923 t = 1.354065923 Simplifying t = 1.354065923Subproblem 2
t + 0.8 = -2.154065923 Simplifying t + 0.8 = -2.154065923 Reorder the terms: 0.8 + t = -2.154065923 Solving 0.8 + t = -2.154065923 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = -2.154065923 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = -2.154065923 + -0.8 t = -2.154065923 + -0.8 Combine like terms: -2.154065923 + -0.8 = -2.954065923 t = -2.954065923 Simplifying t = -2.954065923Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.354065923, -2.954065923}
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