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Simplifying 4t2 + 3t + -35 = 0 Reorder the terms: -35 + 3t + 4t2 = 0 Solving -35 + 3t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 0.75t + t2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 0.75t + 8.75 + t2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 0.75t + t2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 0.75t + t2 = 0 + 8.75 0.75t + t2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 0.75t + t2 = 8.75 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = 8.75 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = 8.75 + 0.140625 Combine like terms: 8.75 + 0.140625 = 8.890625 0.140625 + 0.75t + t2 = 8.890625 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = 8.890625 Calculate the square root of the right side: 2.98171511 Break this problem into two subproblems by setting (t + 0.375) equal to 2.98171511 and -2.98171511.Subproblem 1
t + 0.375 = 2.98171511 Simplifying t + 0.375 = 2.98171511 Reorder the terms: 0.375 + t = 2.98171511 Solving 0.375 + t = 2.98171511 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = 2.98171511 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = 2.98171511 + -0.375 t = 2.98171511 + -0.375 Combine like terms: 2.98171511 + -0.375 = 2.60671511 t = 2.60671511 Simplifying t = 2.60671511Subproblem 2
t + 0.375 = -2.98171511 Simplifying t + 0.375 = -2.98171511 Reorder the terms: 0.375 + t = -2.98171511 Solving 0.375 + t = -2.98171511 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = -2.98171511 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = -2.98171511 + -0.375 t = -2.98171511 + -0.375 Combine like terms: -2.98171511 + -0.375 = -3.35671511 t = -3.35671511 Simplifying t = -3.35671511Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.60671511, -3.35671511}
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