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Simplifying -16t2 + -12t + 60 = 0 Reorder the terms: 60 + -12t + -16t2 = 0 Solving 60 + -12t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + -3t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + -3t + -4t2)' equal to zero and attempt to solve: Simplifying 15 + -3t + -4t2 = 0 Solving 15 + -3t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.75 + 0.75t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 0.75t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 0.75t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 0.75t + t2 = 0 + 3.75 0.75t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 0.75t + t2 = 3.75 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 = 3.75 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = 3.75 + 0.140625 Combine like terms: 3.75 + 0.140625 = 3.890625 0.140625 + 0.75t + t2 = 3.890625 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (t + 0.375) equal to 1.97246673 and -1.97246673.Subproblem 1
t + 0.375 = 1.97246673 Simplifying t + 0.375 = 1.97246673 Reorder the terms: 0.375 + t = 1.97246673 Solving 0.375 + t = 1.97246673 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 = 1.97246673 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = 1.97246673 + -0.375 t = 1.97246673 + -0.375 Combine like terms: 1.97246673 + -0.375 = 1.59746673 t = 1.59746673 Simplifying t = 1.59746673Subproblem 2
t + 0.375 = -1.97246673 Simplifying t + 0.375 = -1.97246673 Reorder the terms: 0.375 + t = -1.97246673 Solving 0.375 + t = -1.97246673 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 = -1.97246673 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = -1.97246673 + -0.375 t = -1.97246673 + -0.375 Combine like terms: -1.97246673 + -0.375 = -2.34746673 t = -2.34746673 Simplifying t = -2.34746673Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.59746673, -2.34746673}Solution
t = {1.59746673, -2.34746673}
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