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Simplifying 6 + 60t + -16t2 = 0 Solving 6 + 60t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 30t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 30t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + 30t + -8t2 = 0 Solving 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 = 3.84746673 t = 3.84746673 Simplifying t = 3.84746673Subproblem 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 = -0.09746673 t = -0.09746673 Simplifying t = -0.09746673Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.84746673, -0.09746673}Solution
t = {3.84746673, -0.09746673}
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