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Simplifying 148 = -16t2 + 96t + 12 Reorder the terms: 148 = 12 + 96t + -16t2 Solving 148 = 12 + 96t + -16t2 Solving for variable 't'. Combine like terms: 148 + -12 = 136 136 + -96t + 16t2 = 12 + 96t + -16t2 + -12 + -96t + 16t2 Reorder the terms: 136 + -96t + 16t2 = 12 + -12 + 96t + -96t + -16t2 + 16t2 Combine like terms: 12 + -12 = 0 136 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 136 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 136 + -96t + 16t2 = 0 + -16t2 + 16t2 136 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 136 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(17 + -12t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(17 + -12t + 2t2)' equal to zero and attempt to solve: Simplifying 17 + -12t + 2t2 = 0 Solving 17 + -12t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -6t + t2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -6t + -8.5 + t2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -6t + t2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -6t + t2 = 0 + -8.5 -6t + t2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -6t + t2 = -8.5 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 = -8.5 + 9 Reorder the terms: 9 + -6t + t2 = -8.5 + 9 Combine like terms: -8.5 + 9 = 0.5 9 + -6t + t2 = 0.5 Factor a perfect square on the left side: (t + -3)(t + -3) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (t + -3) equal to 0.707106781 and -0.707106781.Subproblem 1
t + -3 = 0.707106781 Simplifying t + -3 = 0.707106781 Reorder the terms: -3 + t = 0.707106781 Solving -3 + t = 0.707106781 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 = 0.707106781 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0.707106781 + 3 t = 0.707106781 + 3 Combine like terms: 0.707106781 + 3 = 3.707106781 t = 3.707106781 Simplifying t = 3.707106781Subproblem 2
t + -3 = -0.707106781 Simplifying t + -3 = -0.707106781 Reorder the terms: -3 + t = -0.707106781 Solving -3 + t = -0.707106781 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 = -0.707106781 + 3 Combine like terms: -3 + 3 = 0 0 + t = -0.707106781 + 3 t = -0.707106781 + 3 Combine like terms: -0.707106781 + 3 = 2.292893219 t = 2.292893219 Simplifying t = 2.292893219Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.707106781, 2.292893219}Solution
t = {3.707106781, 2.292893219}
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