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Simplifying -16t2 + 96t + 6 = 0 Reorder the terms: 6 + 96t + -16t2 = 0 Solving 6 + 96t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 48t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 48t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + 48t + -8t2 = 0 Solving 3 + 48t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -6t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -6t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -6t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -6t + t2 = 0 + 0.375 -6t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -6t + t2 = 0.375 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 0.375 + 9 Reorder the terms: 9 + -6t + t2 = 0.375 + 9 Combine like terms: 0.375 + 9 = 9.375 9 + -6t + t2 = 9.375 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.375 Calculate the square root of the right side: 3.061862178 Break this problem into two subproblems by setting (t + -3) equal to 3.061862178 and -3.061862178.Subproblem 1
t + -3 = 3.061862178 Simplifying t + -3 = 3.061862178 Reorder the terms: -3 + t = 3.061862178 Solving -3 + t = 3.061862178 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.061862178 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.061862178 + 3 t = 3.061862178 + 3 Combine like terms: 3.061862178 + 3 = 6.061862178 t = 6.061862178 Simplifying t = 6.061862178Subproblem 2
t + -3 = -3.061862178 Simplifying t + -3 = -3.061862178 Reorder the terms: -3 + t = -3.061862178 Solving -3 + t = -3.061862178 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.061862178 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.061862178 + 3 t = -3.061862178 + 3 Combine like terms: -3.061862178 + 3 = -0.061862178 t = -0.061862178 Simplifying t = -0.061862178Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.061862178, -0.061862178}Solution
t = {6.061862178, -0.061862178}
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