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Simplifying 16t2 + 150t + 110 = 0 Reorder the terms: 110 + 150t + 16t2 = 0 Solving 110 + 150t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(55 + 75t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + 75t + 8t2)' equal to zero and attempt to solve: Simplifying 55 + 75t + 8t2 = 0 Solving 55 + 75t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.875 + 9.375t + t2 = 0 Move the constant term to the right: Add '-6.875' to each side of the equation. 6.875 + 9.375t + -6.875 + t2 = 0 + -6.875 Reorder the terms: 6.875 + -6.875 + 9.375t + t2 = 0 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + 9.375t + t2 = 0 + -6.875 9.375t + t2 = 0 + -6.875 Combine like terms: 0 + -6.875 = -6.875 9.375t + t2 = -6.875 The t term is 9.375t. Take half its coefficient (4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. 9.375t + 21.97265625 + t2 = -6.875 + 21.97265625 Reorder the terms: 21.97265625 + 9.375t + t2 = -6.875 + 21.97265625 Combine like terms: -6.875 + 21.97265625 = 15.09765625 21.97265625 + 9.375t + t2 = 15.09765625 Factor a perfect square on the left side: (t + 4.6875)(t + 4.6875) = 15.09765625 Calculate the square root of the right side: 3.885570261 Break this problem into two subproblems by setting (t + 4.6875) equal to 3.885570261 and -3.885570261.Subproblem 1
t + 4.6875 = 3.885570261 Simplifying t + 4.6875 = 3.885570261 Reorder the terms: 4.6875 + t = 3.885570261 Solving 4.6875 + t = 3.885570261 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + t = 3.885570261 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + t = 3.885570261 + -4.6875 t = 3.885570261 + -4.6875 Combine like terms: 3.885570261 + -4.6875 = -0.801929739 t = -0.801929739 Simplifying t = -0.801929739Subproblem 2
t + 4.6875 = -3.885570261 Simplifying t + 4.6875 = -3.885570261 Reorder the terms: 4.6875 + t = -3.885570261 Solving 4.6875 + t = -3.885570261 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + t = -3.885570261 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + t = -3.885570261 + -4.6875 t = -3.885570261 + -4.6875 Combine like terms: -3.885570261 + -4.6875 = -8.573070261 t = -8.573070261 Simplifying t = -8.573070261Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.801929739, -8.573070261}Solution
t = {-0.801929739, -8.573070261}
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