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Simplifying 0 = -16t2 + 112t + 6 Reorder the terms: 0 = 6 + 112t + -16t2 Solving 0 = 6 + 112t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -112t + 16t2 = 6 + 112t + -16t2 + -6 + -112t + 16t2 Reorder the terms: -6 + -112t + 16t2 = 6 + -6 + 112t + -112t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2 -6 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2 Combine like terms: 112t + -112t = 0 -6 + -112t + 16t2 = 0 + -16t2 + 16t2 -6 + -112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -112t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -56t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -56t + 8t2)' equal to zero and attempt to solve: Simplifying -3 + -56t + 8t2 = 0 Solving -3 + -56t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -7t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -7t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -7t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -7t + t2 = 0 + 0.375 -7t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -7t + t2 = 0.375 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = 0.375 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 0.375 + 12.25 Combine like terms: 0.375 + 12.25 = 12.625 12.25 + -7t + t2 = 12.625 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 12.625 Calculate the square root of the right side: 3.553167601 Break this problem into two subproblems by setting (t + -3.5) equal to 3.553167601 and -3.553167601.Subproblem 1
t + -3.5 = 3.553167601 Simplifying t + -3.5 = 3.553167601 Reorder the terms: -3.5 + t = 3.553167601 Solving -3.5 + t = 3.553167601 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.553167601 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.553167601 + 3.5 t = 3.553167601 + 3.5 Combine like terms: 3.553167601 + 3.5 = 7.053167601 t = 7.053167601 Simplifying t = 7.053167601Subproblem 2
t + -3.5 = -3.553167601 Simplifying t + -3.5 = -3.553167601 Reorder the terms: -3.5 + t = -3.553167601 Solving -3.5 + t = -3.553167601 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.553167601 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.553167601 + 3.5 t = -3.553167601 + 3.5 Combine like terms: -3.553167601 + 3.5 = -0.053167601 t = -0.053167601 Simplifying t = -0.053167601Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.053167601, -0.053167601}Solution
t = {7.053167601, -0.053167601}
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