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Simplifying 96 = 16t2 + 88t Reorder the terms: 96 = 88t + 16t2 Solving 96 = 88t + 16t2 Solving for variable 't'. Reorder the terms: 96 + -88t + -16t2 = 88t + -88t + 16t2 + -16t2 Combine like terms: 88t + -88t = 0 96 + -88t + -16t2 = 0 + 16t2 + -16t2 96 + -88t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 96 + -88t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(12 + -11t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(12 + -11t + -2t2)' equal to zero and attempt to solve: Simplifying 12 + -11t + -2t2 = 0 Solving 12 + -11t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + 5.5t + t2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 5.5t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + 5.5t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5.5t + t2 = 0 + 6 5.5t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 5.5t + t2 = 6 The t term is 5.5t. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5t + 7.5625 + t2 = 6 + 7.5625 Reorder the terms: 7.5625 + 5.5t + t2 = 6 + 7.5625 Combine like terms: 6 + 7.5625 = 13.5625 7.5625 + 5.5t + t2 = 13.5625 Factor a perfect square on the left side: (t + 2.75)(t + 2.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (t + 2.75) equal to 3.682729966 and -3.682729966.Subproblem 1
t + 2.75 = 3.682729966 Simplifying t + 2.75 = 3.682729966 Reorder the terms: 2.75 + t = 3.682729966 Solving 2.75 + t = 3.682729966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = 3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = 3.682729966 + -2.75 t = 3.682729966 + -2.75 Combine like terms: 3.682729966 + -2.75 = 0.932729966 t = 0.932729966 Simplifying t = 0.932729966Subproblem 2
t + 2.75 = -3.682729966 Simplifying t + 2.75 = -3.682729966 Reorder the terms: 2.75 + t = -3.682729966 Solving 2.75 + t = -3.682729966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = -3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = -3.682729966 + -2.75 t = -3.682729966 + -2.75 Combine like terms: -3.682729966 + -2.75 = -6.432729966 t = -6.432729966 Simplifying t = -6.432729966Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.932729966, -6.432729966}Solution
t = {0.932729966, -6.432729966}
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