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Simplifying -16t2 + 96t + 50 = 0 Reorder the terms: 50 + 96t + -16t2 = 0 Solving 50 + 96t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 48t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 48t + -8t2)' equal to zero and attempt to solve: Simplifying 25 + 48t + -8t2 = 0 Solving 25 + 48t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -6t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -6t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -6t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -6t + t2 = 0 + 3.125 -6t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -6t + t2 = 3.125 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 = 3.125 + 9 Reorder the terms: 9 + -6t + t2 = 3.125 + 9 Combine like terms: 3.125 + 9 = 12.125 9 + -6t + t2 = 12.125 Factor a perfect square on the left side: (t + -3)(t + -3) = 12.125 Calculate the square root of the right side: 3.482097069 Break this problem into two subproblems by setting (t + -3) equal to 3.482097069 and -3.482097069.Subproblem 1
t + -3 = 3.482097069 Simplifying t + -3 = 3.482097069 Reorder the terms: -3 + t = 3.482097069 Solving -3 + t = 3.482097069 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 = 3.482097069 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.482097069 + 3 t = 3.482097069 + 3 Combine like terms: 3.482097069 + 3 = 6.482097069 t = 6.482097069 Simplifying t = 6.482097069Subproblem 2
t + -3 = -3.482097069 Simplifying t + -3 = -3.482097069 Reorder the terms: -3 + t = -3.482097069 Solving -3 + t = -3.482097069 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 = -3.482097069 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.482097069 + 3 t = -3.482097069 + 3 Combine like terms: -3.482097069 + 3 = -0.482097069 t = -0.482097069 Simplifying t = -0.482097069Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.482097069, -0.482097069}Solution
t = {6.482097069, -0.482097069}
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