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Simplifying 12t2 + 19t = 6 Reorder the terms: 19t + 12t2 = 6 Solving 19t + 12t2 = 6 Solving for variable 't'. Reorder the terms: -6 + 19t + 12t2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 19t + 12t2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5 + 1.583333333t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.583333333t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.583333333t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.583333333t + t2 = 0 + 0.5 1.583333333t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.583333333t + t2 = 0.5 The t term is 1.583333333t. Take half its coefficient (0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. 1.583333333t + 0.6267361108 + t2 = 0.5 + 0.6267361108 Reorder the terms: 0.6267361108 + 1.583333333t + t2 = 0.5 + 0.6267361108 Combine like terms: 0.5 + 0.6267361108 = 1.1267361108 0.6267361108 + 1.583333333t + t2 = 1.1267361108 Factor a perfect square on the left side: (t + 0.7916666665)(t + 0.7916666665) = 1.1267361108 Calculate the square root of the right side: 1.061478267 Break this problem into two subproblems by setting (t + 0.7916666665) equal to 1.061478267 and -1.061478267.Subproblem 1
t + 0.7916666665 = 1.061478267 Simplifying t + 0.7916666665 = 1.061478267 Reorder the terms: 0.7916666665 + t = 1.061478267 Solving 0.7916666665 + t = 1.061478267 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7916666665' to each side of the equation. 0.7916666665 + -0.7916666665 + t = 1.061478267 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + t = 1.061478267 + -0.7916666665 t = 1.061478267 + -0.7916666665 Combine like terms: 1.061478267 + -0.7916666665 = 0.2698116005 t = 0.2698116005 Simplifying t = 0.2698116005Subproblem 2
t + 0.7916666665 = -1.061478267 Simplifying t + 0.7916666665 = -1.061478267 Reorder the terms: 0.7916666665 + t = -1.061478267 Solving 0.7916666665 + t = -1.061478267 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7916666665' to each side of the equation. 0.7916666665 + -0.7916666665 + t = -1.061478267 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + t = -1.061478267 + -0.7916666665 t = -1.061478267 + -0.7916666665 Combine like terms: -1.061478267 + -0.7916666665 = -1.8531449335 t = -1.8531449335 Simplifying t = -1.8531449335Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.2698116005, -1.8531449335}
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