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Simplifying -120 = -16t2 + 96t Reorder the terms: -120 = 96t + -16t2 Solving -120 = 96t + -16t2 Solving for variable 't'. Reorder the terms: -120 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -120 + -96t + 16t2 = 0 + -16t2 + 16t2 -120 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -120 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-15 + -12t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-15 + -12t + 2t2)' equal to zero and attempt to solve: Simplifying -15 + -12t + 2t2 = 0 Solving -15 + -12t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -6t + t2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -6t + 7.5 + t2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -6t + t2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -6t + t2 = 0 + 7.5 -6t + t2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -6t + t2 = 7.5 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 = 7.5 + 9 Reorder the terms: 9 + -6t + t2 = 7.5 + 9 Combine like terms: 7.5 + 9 = 16.5 9 + -6t + t2 = 16.5 Factor a perfect square on the left side: (t + -3)(t + -3) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (t + -3) equal to 4.062019202 and -4.062019202.Subproblem 1
t + -3 = 4.062019202 Simplifying t + -3 = 4.062019202 Reorder the terms: -3 + t = 4.062019202 Solving -3 + t = 4.062019202 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 = 4.062019202 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.062019202 + 3 t = 4.062019202 + 3 Combine like terms: 4.062019202 + 3 = 7.062019202 t = 7.062019202 Simplifying t = 7.062019202Subproblem 2
t + -3 = -4.062019202 Simplifying t + -3 = -4.062019202 Reorder the terms: -3 + t = -4.062019202 Solving -3 + t = -4.062019202 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 = -4.062019202 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.062019202 + 3 t = -4.062019202 + 3 Combine like terms: -4.062019202 + 3 = -1.062019202 t = -1.062019202 Simplifying t = -1.062019202Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.062019202, -1.062019202}Solution
t = {7.062019202, -1.062019202}
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