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Simplifying 3 = 8t2 + 30t Reorder the terms: 3 = 30t + 8t2 Solving 3 = 30t + 8t2 Solving for variable 't'. Reorder the terms: 3 + -30t + -8t2 = 30t + -30t + 8t2 + -8t2 Combine like terms: 30t + -30t = 0 3 + -30t + -8t2 = 0 + 8t2 + -8t2 3 + -30t + -8t2 = 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 3 + -30t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + 3.75t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 3.75t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 3.75t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 3.75t + t2 = 0 + 0.375 3.75t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 3.75t + t2 = 0.375 The t term is 3.75t. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75t + 3.515625 + t2 = 0.375 + 3.515625 Reorder the terms: 3.515625 + 3.75t + t2 = 0.375 + 3.515625 Combine like terms: 0.375 + 3.515625 = 3.890625 3.515625 + 3.75t + t2 = 3.890625 Factor a perfect square on the left side: (t + 1.875)(t + 1.875) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (t + 1.875) equal to 1.97246673 and -1.97246673.Subproblem 1
t + 1.875 = 1.97246673 Simplifying t + 1.875 = 1.97246673 Reorder the terms: 1.875 + t = 1.97246673 Solving 1.875 + t = 1.97246673 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = 1.97246673 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = 1.97246673 + -1.875 t = 1.97246673 + -1.875 Combine like terms: 1.97246673 + -1.875 = 0.09746673 t = 0.09746673 Simplifying t = 0.09746673Subproblem 2
t + 1.875 = -1.97246673 Simplifying t + 1.875 = -1.97246673 Reorder the terms: 1.875 + t = -1.97246673 Solving 1.875 + t = -1.97246673 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = -1.97246673 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = -1.97246673 + -1.875 t = -1.97246673 + -1.875 Combine like terms: -1.97246673 + -1.875 = -3.84746673 t = -3.84746673 Simplifying t = -3.84746673Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.09746673, -3.84746673}
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