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Simplifying 0 = -16t2 + 34t + 2 Reorder the terms: 0 = 2 + 34t + -16t2 Solving 0 = 2 + 34t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -34t + 16t2 = 2 + 34t + -16t2 + -2 + -34t + 16t2 Reorder the terms: -2 + -34t + 16t2 = 2 + -2 + 34t + -34t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + -34t + 16t2 = 0 + 34t + -34t + -16t2 + 16t2 -2 + -34t + 16t2 = 34t + -34t + -16t2 + 16t2 Combine like terms: 34t + -34t = 0 -2 + -34t + 16t2 = 0 + -16t2 + 16t2 -2 + -34t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + -34t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -17t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -17t + 8t2)' equal to zero and attempt to solve: Simplifying -1 + -17t + 8t2 = 0 Solving -1 + -17t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -2.125t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -2.125t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -2.125t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -2.125t + t2 = 0 + 0.125 -2.125t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -2.125t + t2 = 0.125 The t term is -2.125t. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125t + 1.12890625 + t2 = 0.125 + 1.12890625 Reorder the terms: 1.12890625 + -2.125t + t2 = 0.125 + 1.12890625 Combine like terms: 0.125 + 1.12890625 = 1.25390625 1.12890625 + -2.125t + t2 = 1.25390625 Factor a perfect square on the left side: (t + -1.0625)(t + -1.0625) = 1.25390625 Calculate the square root of the right side: 1.119779554 Break this problem into two subproblems by setting (t + -1.0625) equal to 1.119779554 and -1.119779554.Subproblem 1
t + -1.0625 = 1.119779554 Simplifying t + -1.0625 = 1.119779554 Reorder the terms: -1.0625 + t = 1.119779554 Solving -1.0625 + t = 1.119779554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + t = 1.119779554 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + t = 1.119779554 + 1.0625 t = 1.119779554 + 1.0625 Combine like terms: 1.119779554 + 1.0625 = 2.182279554 t = 2.182279554 Simplifying t = 2.182279554Subproblem 2
t + -1.0625 = -1.119779554 Simplifying t + -1.0625 = -1.119779554 Reorder the terms: -1.0625 + t = -1.119779554 Solving -1.0625 + t = -1.119779554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + t = -1.119779554 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + t = -1.119779554 + 1.0625 t = -1.119779554 + 1.0625 Combine like terms: -1.119779554 + 1.0625 = -0.057279554 t = -0.057279554 Simplifying t = -0.057279554Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.182279554, -0.057279554}Solution
t = {2.182279554, -0.057279554}
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