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Simplifying 8t2 + 5t + -75 = 0 Reorder the terms: -75 + 5t + 8t2 = 0 Solving -75 + 5t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -9.375 + 0.625t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 0.625t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 0.625t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 0.625t + t2 = 0 + 9.375 0.625t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 0.625t + t2 = 9.375 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 9.375 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 9.375 + 0.09765625 Combine like terms: 9.375 + 0.09765625 = 9.47265625 0.09765625 + 0.625t + t2 = 9.47265625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 9.47265625 Calculate the square root of the right side: 3.077768063 Break this problem into two subproblems by setting (t + 0.3125) equal to 3.077768063 and -3.077768063.Subproblem 1
t + 0.3125 = 3.077768063 Simplifying t + 0.3125 = 3.077768063 Reorder the terms: 0.3125 + t = 3.077768063 Solving 0.3125 + t = 3.077768063 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 3.077768063 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 3.077768063 + -0.3125 t = 3.077768063 + -0.3125 Combine like terms: 3.077768063 + -0.3125 = 2.765268063 t = 2.765268063 Simplifying t = 2.765268063Subproblem 2
t + 0.3125 = -3.077768063 Simplifying t + 0.3125 = -3.077768063 Reorder the terms: 0.3125 + t = -3.077768063 Solving 0.3125 + t = -3.077768063 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -3.077768063 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -3.077768063 + -0.3125 t = -3.077768063 + -0.3125 Combine like terms: -3.077768063 + -0.3125 = -3.390268063 t = -3.390268063 Simplifying t = -3.390268063Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.765268063, -3.390268063}
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