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Simplifying -16t2 + 130t + 6 = 0 Reorder the terms: 6 + 130t + -16t2 = 0 Solving 6 + 130t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 65t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 65t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + 65t + -8t2 = 0 Solving 3 + 65t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -8.125t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -8.125t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -8.125t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -8.125t + t2 = 0 + 0.375 -8.125t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -8.125t + t2 = 0.375 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 = 0.375 + 16.50390625 Reorder the terms: 16.50390625 + -8.125t + t2 = 0.375 + 16.50390625 Combine like terms: 0.375 + 16.50390625 = 16.87890625 16.50390625 + -8.125t + t2 = 16.87890625 Factor a perfect square on the left side: (t + -4.0625)(t + -4.0625) = 16.87890625 Calculate the square root of the right side: 4.108394607 Break this problem into two subproblems by setting (t + -4.0625) equal to 4.108394607 and -4.108394607.Subproblem 1
t + -4.0625 = 4.108394607 Simplifying t + -4.0625 = 4.108394607 Reorder the terms: -4.0625 + t = 4.108394607 Solving -4.0625 + t = 4.108394607 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 = 4.108394607 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + t = 4.108394607 + 4.0625 t = 4.108394607 + 4.0625 Combine like terms: 4.108394607 + 4.0625 = 8.170894607 t = 8.170894607 Simplifying t = 8.170894607Subproblem 2
t + -4.0625 = -4.108394607 Simplifying t + -4.0625 = -4.108394607 Reorder the terms: -4.0625 + t = -4.108394607 Solving -4.0625 + t = -4.108394607 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 = -4.108394607 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + t = -4.108394607 + 4.0625 t = -4.108394607 + 4.0625 Combine like terms: -4.108394607 + 4.0625 = -0.045894607 t = -0.045894607 Simplifying t = -0.045894607Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.170894607, -0.045894607}Solution
t = {8.170894607, -0.045894607}
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