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Simplifying -16t2 + 130t + 2 = 0 Reorder the terms: 2 + 130t + -16t2 = 0 Solving 2 + 130t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 65t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 65t + -8t2)' equal to zero and attempt to solve: Simplifying 1 + 65t + -8t2 = 0 Solving 1 + 65t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + -8.125t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -8.125t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -8.125t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -8.125t + t2 = 0 + 0.125 -8.125t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -8.125t + t2 = 0.125 The t term is -8.125t. Take half its coefficient (-4.0625). Square it (16.50390625) and add it to both sides. Add '16.50390625' to each side of the equation. -8.125t + 16.50390625 + t2 = 0.125 + 16.50390625 Reorder the terms: 16.50390625 + -8.125t + t2 = 0.125 + 16.50390625 Combine like terms: 0.125 + 16.50390625 = 16.62890625 16.50390625 + -8.125t + t2 = 16.62890625 Factor a perfect square on the left side: (t + -4.0625)(t + -4.0625) = 16.62890625 Calculate the square root of the right side: 4.077855595 Break this problem into two subproblems by setting (t + -4.0625) equal to 4.077855595 and -4.077855595.Subproblem 1
t + -4.0625 = 4.077855595 Simplifying t + -4.0625 = 4.077855595 Reorder the terms: -4.0625 + t = 4.077855595 Solving -4.0625 + t = 4.077855595 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.0625' to each side of the equation. -4.0625 + 4.0625 + t = 4.077855595 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + t = 4.077855595 + 4.0625 t = 4.077855595 + 4.0625 Combine like terms: 4.077855595 + 4.0625 = 8.140355595 t = 8.140355595 Simplifying t = 8.140355595Subproblem 2
t + -4.0625 = -4.077855595 Simplifying t + -4.0625 = -4.077855595 Reorder the terms: -4.0625 + t = -4.077855595 Solving -4.0625 + t = -4.077855595 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.0625' to each side of the equation. -4.0625 + 4.0625 + t = -4.077855595 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + t = -4.077855595 + 4.0625 t = -4.077855595 + 4.0625 Combine like terms: -4.077855595 + 4.0625 = -0.015355595 t = -0.015355595 Simplifying t = -0.015355595Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.140355595, -0.015355595}Solution
t = {8.140355595, -0.015355595}
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