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Simplifying 16t2 + 88t + 48 = 0 Reorder the terms: 48 + 88t + 16t2 = 0 Solving 48 + 88t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(6 + 11t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(6 + 11t + 2t2)' equal to zero and attempt to solve: Simplifying 6 + 11t + 2t2 = 0 Solving 6 + 11t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 5.5t + t2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 5.5t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + 5.5t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5.5t + t2 = 0 + -3 5.5t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 5.5t + t2 = -3 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 = -3 + 7.5625 Reorder the terms: 7.5625 + 5.5t + t2 = -3 + 7.5625 Combine like terms: -3 + 7.5625 = 4.5625 7.5625 + 5.5t + t2 = 4.5625 Factor a perfect square on the left side: (t + 2.75)(t + 2.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (t + 2.75) equal to 2.136000936 and -2.136000936.Subproblem 1
t + 2.75 = 2.136000936 Simplifying t + 2.75 = 2.136000936 Reorder the terms: 2.75 + t = 2.136000936 Solving 2.75 + t = 2.136000936 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 = 2.136000936 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = 2.136000936 + -2.75 t = 2.136000936 + -2.75 Combine like terms: 2.136000936 + -2.75 = -0.613999064 t = -0.613999064 Simplifying t = -0.613999064Subproblem 2
t + 2.75 = -2.136000936 Simplifying t + 2.75 = -2.136000936 Reorder the terms: 2.75 + t = -2.136000936 Solving 2.75 + t = -2.136000936 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 = -2.136000936 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = -2.136000936 + -2.75 t = -2.136000936 + -2.75 Combine like terms: -2.136000936 + -2.75 = -4.886000936 t = -4.886000936 Simplifying t = -4.886000936Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.613999064, -4.886000936}Solution
t = {-0.613999064, -4.886000936}
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