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Simplifying 0.8t2 + 12t + -45 = 0 Reorder the terms: -45 + 12t + 0.8t2 = 0 Solving -45 + 12t + 0.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -56.25 + 15t + t2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + 15t + 56.25 + t2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + 15t + t2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + 15t + t2 = 0 + 56.25 15t + t2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 15t + t2 = 56.25 The t term is 15t. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15t + 56.25 + t2 = 56.25 + 56.25 Reorder the terms: 56.25 + 15t + t2 = 56.25 + 56.25 Combine like terms: 56.25 + 56.25 = 112.5 56.25 + 15t + t2 = 112.5 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 112.5 Calculate the square root of the right side: 10.606601718 Break this problem into two subproblems by setting (t + 7.5) equal to 10.606601718 and -10.606601718.Subproblem 1
t + 7.5 = 10.606601718 Simplifying t + 7.5 = 10.606601718 Reorder the terms: 7.5 + t = 10.606601718 Solving 7.5 + t = 10.606601718 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = 10.606601718 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 10.606601718 + -7.5 t = 10.606601718 + -7.5 Combine like terms: 10.606601718 + -7.5 = 3.106601718 t = 3.106601718 Simplifying t = 3.106601718Subproblem 2
t + 7.5 = -10.606601718 Simplifying t + 7.5 = -10.606601718 Reorder the terms: 7.5 + t = -10.606601718 Solving 7.5 + t = -10.606601718 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = -10.606601718 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -10.606601718 + -7.5 t = -10.606601718 + -7.5 Combine like terms: -10.606601718 + -7.5 = -18.106601718 t = -18.106601718 Simplifying t = -18.106601718Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.106601718, -18.106601718}
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