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Simplifying 4t2 + -35t + -40 = 0 Reorder the terms: -40 + -35t + 4t2 = 0 Solving -40 + -35t + 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'. -10 + -8.75t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -8.75t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -8.75t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -8.75t + t2 = 0 + 10 -8.75t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -8.75t + t2 = 10 The t term is -8.75t. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75t + 19.140625 + t2 = 10 + 19.140625 Reorder the terms: 19.140625 + -8.75t + t2 = 10 + 19.140625 Combine like terms: 10 + 19.140625 = 29.140625 19.140625 + -8.75t + t2 = 29.140625 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 29.140625 Calculate the square root of the right side: 5.39820572 Break this problem into two subproblems by setting (t + -4.375) equal to 5.39820572 and -5.39820572.Subproblem 1
t + -4.375 = 5.39820572 Simplifying t + -4.375 = 5.39820572 Reorder the terms: -4.375 + t = 5.39820572 Solving -4.375 + t = 5.39820572 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = 5.39820572 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 5.39820572 + 4.375 t = 5.39820572 + 4.375 Combine like terms: 5.39820572 + 4.375 = 9.77320572 t = 9.77320572 Simplifying t = 9.77320572Subproblem 2
t + -4.375 = -5.39820572 Simplifying t + -4.375 = -5.39820572 Reorder the terms: -4.375 + t = -5.39820572 Solving -4.375 + t = -5.39820572 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = -5.39820572 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -5.39820572 + 4.375 t = -5.39820572 + 4.375 Combine like terms: -5.39820572 + 4.375 = -1.02320572 t = -1.02320572 Simplifying t = -1.02320572Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.77320572, -1.02320572}
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