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Simplifying 128t + -16t2 = 50 Solving 128t + -16t2 = 50 Solving for variable 't'. Reorder the terms: -50 + 128t + -16t2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 128t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 64t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 64t + -8t2)' equal to zero and attempt to solve: Simplifying -25 + 64t + -8t2 = 0 Solving -25 + 64t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 3.125 + -8t + t2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -8t + -3.125 + t2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -8t + t2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -8t + t2 = 0 + -3.125 -8t + t2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -8t + t2 = -3.125 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -3.125 + 16 Reorder the terms: 16 + -8t + t2 = -3.125 + 16 Combine like terms: -3.125 + 16 = 12.875 16 + -8t + t2 = 12.875 Factor a perfect square on the left side: (t + -4)(t + -4) = 12.875 Calculate the square root of the right side: 3.588175024 Break this problem into two subproblems by setting (t + -4) equal to 3.588175024 and -3.588175024.Subproblem 1
t + -4 = 3.588175024 Simplifying t + -4 = 3.588175024 Reorder the terms: -4 + t = 3.588175024 Solving -4 + t = 3.588175024 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.588175024 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.588175024 + 4 t = 3.588175024 + 4 Combine like terms: 3.588175024 + 4 = 7.588175024 t = 7.588175024 Simplifying t = 7.588175024Subproblem 2
t + -4 = -3.588175024 Simplifying t + -4 = -3.588175024 Reorder the terms: -4 + t = -3.588175024 Solving -4 + t = -3.588175024 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.588175024 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.588175024 + 4 t = -3.588175024 + 4 Combine like terms: -3.588175024 + 4 = 0.411824976 t = 0.411824976 Simplifying t = 0.411824976Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.588175024, 0.411824976}Solution
t = {7.588175024, 0.411824976}
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