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Simplifying 0 = -16t2 + 64t + 334 Reorder the terms: 0 = 334 + 64t + -16t2 Solving 0 = 334 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -334 = -334 -334 + -64t + 16t2 = 334 + 64t + -16t2 + -334 + -64t + 16t2 Reorder the terms: -334 + -64t + 16t2 = 334 + -334 + 64t + -64t + -16t2 + 16t2 Combine like terms: 334 + -334 = 0 -334 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -334 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -334 + -64t + 16t2 = 0 + -16t2 + 16t2 -334 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -334 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-167 + -32t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-167 + -32t + 8t2)' equal to zero and attempt to solve: Simplifying -167 + -32t + 8t2 = 0 Solving -167 + -32t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -20.875 + -4t + t2 = 0 Move the constant term to the right: Add '20.875' to each side of the equation. -20.875 + -4t + 20.875 + t2 = 0 + 20.875 Reorder the terms: -20.875 + 20.875 + -4t + t2 = 0 + 20.875 Combine like terms: -20.875 + 20.875 = 0.000 0.000 + -4t + t2 = 0 + 20.875 -4t + t2 = 0 + 20.875 Combine like terms: 0 + 20.875 = 20.875 -4t + t2 = 20.875 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 20.875 + 4 Reorder the terms: 4 + -4t + t2 = 20.875 + 4 Combine like terms: 20.875 + 4 = 24.875 4 + -4t + t2 = 24.875 Factor a perfect square on the left side: (t + -2)(t + -2) = 24.875 Calculate the square root of the right side: 4.987484336 Break this problem into two subproblems by setting (t + -2) equal to 4.987484336 and -4.987484336.Subproblem 1
t + -2 = 4.987484336 Simplifying t + -2 = 4.987484336 Reorder the terms: -2 + t = 4.987484336 Solving -2 + t = 4.987484336 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 4.987484336 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4.987484336 + 2 t = 4.987484336 + 2 Combine like terms: 4.987484336 + 2 = 6.987484336 t = 6.987484336 Simplifying t = 6.987484336Subproblem 2
t + -2 = -4.987484336 Simplifying t + -2 = -4.987484336 Reorder the terms: -2 + t = -4.987484336 Solving -2 + t = -4.987484336 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -4.987484336 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4.987484336 + 2 t = -4.987484336 + 2 Combine like terms: -4.987484336 + 2 = -2.987484336 t = -2.987484336 Simplifying t = -2.987484336Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.987484336, -2.987484336}Solution
t = {6.987484336, -2.987484336}
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