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Simplifying 16t2 + 96t + 4 = 40 Reorder the terms: 4 + 96t + 16t2 = 40 Solving 4 + 96t + 16t2 = 40 Solving for variable 't'. Reorder the terms: 4 + -40 + 96t + 16t2 = 40 + -40 Combine like terms: 4 + -40 = -36 -36 + 96t + 16t2 = 40 + -40 Combine like terms: 40 + -40 = 0 -36 + 96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + 24t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + 24t + 4t2)' equal to zero and attempt to solve: Simplifying -9 + 24t + 4t2 = 0 Solving -9 + 24t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 6t + t2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 6t + 2.25 + t2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 6t + t2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 6t + t2 = 0 + 2.25 6t + t2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 6t + t2 = 2.25 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 = 2.25 + 9 Reorder the terms: 9 + 6t + t2 = 2.25 + 9 Combine like terms: 2.25 + 9 = 11.25 9 + 6t + t2 = 11.25 Factor a perfect square on the left side: (t + 3)(t + 3) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (t + 3) equal to 3.354101966 and -3.354101966.Subproblem 1
t + 3 = 3.354101966 Simplifying t + 3 = 3.354101966 Reorder the terms: 3 + t = 3.354101966 Solving 3 + t = 3.354101966 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 = 3.354101966 + -3 Combine like terms: 3 + -3 = 0 0 + t = 3.354101966 + -3 t = 3.354101966 + -3 Combine like terms: 3.354101966 + -3 = 0.354101966 t = 0.354101966 Simplifying t = 0.354101966Subproblem 2
t + 3 = -3.354101966 Simplifying t + 3 = -3.354101966 Reorder the terms: 3 + t = -3.354101966 Solving 3 + t = -3.354101966 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 = -3.354101966 + -3 Combine like terms: 3 + -3 = 0 0 + t = -3.354101966 + -3 t = -3.354101966 + -3 Combine like terms: -3.354101966 + -3 = -6.354101966 t = -6.354101966 Simplifying t = -6.354101966Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.354101966, -6.354101966}Solution
t = {0.354101966, -6.354101966}
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