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Simplifying 2t2 + -246t + -1305 = 0 Reorder the terms: -1305 + -246t + 2t2 = 0 Solving -1305 + -246t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -652.5 + -123t + t2 = 0 Move the constant term to the right: Add '652.5' to each side of the equation. -652.5 + -123t + 652.5 + t2 = 0 + 652.5 Reorder the terms: -652.5 + 652.5 + -123t + t2 = 0 + 652.5 Combine like terms: -652.5 + 652.5 = 0.0 0.0 + -123t + t2 = 0 + 652.5 -123t + t2 = 0 + 652.5 Combine like terms: 0 + 652.5 = 652.5 -123t + t2 = 652.5 The t term is -123t. Take half its coefficient (-61.5). Square it (3782.25) and add it to both sides. Add '3782.25' to each side of the equation. -123t + 3782.25 + t2 = 652.5 + 3782.25 Reorder the terms: 3782.25 + -123t + t2 = 652.5 + 3782.25 Combine like terms: 652.5 + 3782.25 = 4434.75 3782.25 + -123t + t2 = 4434.75 Factor a perfect square on the left side: (t + -61.5)(t + -61.5) = 4434.75 Calculate the square root of the right side: 66.593918641 Break this problem into two subproblems by setting (t + -61.5) equal to 66.593918641 and -66.593918641.Subproblem 1
t + -61.5 = 66.593918641 Simplifying t + -61.5 = 66.593918641 Reorder the terms: -61.5 + t = 66.593918641 Solving -61.5 + t = 66.593918641 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '61.5' to each side of the equation. -61.5 + 61.5 + t = 66.593918641 + 61.5 Combine like terms: -61.5 + 61.5 = 0.0 0.0 + t = 66.593918641 + 61.5 t = 66.593918641 + 61.5 Combine like terms: 66.593918641 + 61.5 = 128.093918641 t = 128.093918641 Simplifying t = 128.093918641Subproblem 2
t + -61.5 = -66.593918641 Simplifying t + -61.5 = -66.593918641 Reorder the terms: -61.5 + t = -66.593918641 Solving -61.5 + t = -66.593918641 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '61.5' to each side of the equation. -61.5 + 61.5 + t = -66.593918641 + 61.5 Combine like terms: -61.5 + 61.5 = 0.0 0.0 + t = -66.593918641 + 61.5 t = -66.593918641 + 61.5 Combine like terms: -66.593918641 + 61.5 = -5.093918641 t = -5.093918641 Simplifying t = -5.093918641Solution
The solution to the problem is based on the solutions from the subproblems. t = {128.093918641, -5.093918641}
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