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Simplifying -16t2 + 62t + 6 = 0 Reorder the terms: 6 + 62t + -16t2 = 0 Solving 6 + 62t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 31t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 31t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + 31t + -8t2 = 0 Solving 3 + 31t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -3.875t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3.875t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3.875t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3.875t + t2 = 0 + 0.375 -3.875t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3.875t + t2 = 0.375 The t term is -3.875t. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875t + 3.75390625 + t2 = 0.375 + 3.75390625 Reorder the terms: 3.75390625 + -3.875t + t2 = 0.375 + 3.75390625 Combine like terms: 0.375 + 3.75390625 = 4.12890625 3.75390625 + -3.875t + t2 = 4.12890625 Factor a perfect square on the left side: (t + -1.9375)(t + -1.9375) = 4.12890625 Calculate the square root of the right side: 2.031971026 Break this problem into two subproblems by setting (t + -1.9375) equal to 2.031971026 and -2.031971026.Subproblem 1
t + -1.9375 = 2.031971026 Simplifying t + -1.9375 = 2.031971026 Reorder the terms: -1.9375 + t = 2.031971026 Solving -1.9375 + t = 2.031971026 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = 2.031971026 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = 2.031971026 + 1.9375 t = 2.031971026 + 1.9375 Combine like terms: 2.031971026 + 1.9375 = 3.969471026 t = 3.969471026 Simplifying t = 3.969471026Subproblem 2
t + -1.9375 = -2.031971026 Simplifying t + -1.9375 = -2.031971026 Reorder the terms: -1.9375 + t = -2.031971026 Solving -1.9375 + t = -2.031971026 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = -2.031971026 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = -2.031971026 + 1.9375 t = -2.031971026 + 1.9375 Combine like terms: -2.031971026 + 1.9375 = -0.094471026 t = -0.094471026 Simplifying t = -0.094471026Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.969471026, -0.094471026}Solution
t = {3.969471026, -0.094471026}
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