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Simplifying 5.71t(12.92 + -6.71t) = -14.83 (12.92 * 5.71t + -6.71t * 5.71t) = -14.83 (73.7732t + -38.3141t2) = -14.83 Solving 73.7732t + -38.3141t2 = -14.83 Solving for variable 't'. Reorder the terms: 14.83 + 73.7732t + -38.3141t2 = -14.83 + 14.83 Combine like terms: -14.83 + 14.83 = 0.00 14.83 + 73.7732t + -38.3141t2 = 0.00 Begin completing the square. Divide all terms by -38.3141 the coefficient of the squared term: Divide each side by '-38.3141'. -0.3870637703 + -1.925484352t + t2 = 0 Move the constant term to the right: Add '0.3870637703' to each side of the equation. -0.3870637703 + -1.925484352t + 0.3870637703 + t2 = 0 + 0.3870637703 Reorder the terms: -0.3870637703 + 0.3870637703 + -1.925484352t + t2 = 0 + 0.3870637703 Combine like terms: -0.3870637703 + 0.3870637703 = 0.0000000000 0.0000000000 + -1.925484352t + t2 = 0 + 0.3870637703 -1.925484352t + t2 = 0 + 0.3870637703 Combine like terms: 0 + 0.3870637703 = 0.3870637703 -1.925484352t + t2 = 0.3870637703 The t term is -1.925484352t. Take half its coefficient (-0.962742176). Square it (0.9268724974) and add it to both sides. Add '0.9268724974' to each side of the equation. -1.925484352t + 0.9268724974 + t2 = 0.3870637703 + 0.9268724974 Reorder the terms: 0.9268724974 + -1.925484352t + t2 = 0.3870637703 + 0.9268724974 Combine like terms: 0.3870637703 + 0.9268724974 = 1.3139362677 0.9268724974 + -1.925484352t + t2 = 1.3139362677 Factor a perfect square on the left side: (t + -0.962742176)(t + -0.962742176) = 1.3139362677 Calculate the square root of the right side: 1.146270591 Break this problem into two subproblems by setting (t + -0.962742176) equal to 1.146270591 and -1.146270591.Subproblem 1
t + -0.962742176 = 1.146270591 Simplifying t + -0.962742176 = 1.146270591 Reorder the terms: -0.962742176 + t = 1.146270591 Solving -0.962742176 + t = 1.146270591 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.962742176' to each side of the equation. -0.962742176 + 0.962742176 + t = 1.146270591 + 0.962742176 Combine like terms: -0.962742176 + 0.962742176 = 0.000000000 0.000000000 + t = 1.146270591 + 0.962742176 t = 1.146270591 + 0.962742176 Combine like terms: 1.146270591 + 0.962742176 = 2.109012767 t = 2.109012767 Simplifying t = 2.109012767Subproblem 2
t + -0.962742176 = -1.146270591 Simplifying t + -0.962742176 = -1.146270591 Reorder the terms: -0.962742176 + t = -1.146270591 Solving -0.962742176 + t = -1.146270591 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.962742176' to each side of the equation. -0.962742176 + 0.962742176 + t = -1.146270591 + 0.962742176 Combine like terms: -0.962742176 + 0.962742176 = 0.000000000 0.000000000 + t = -1.146270591 + 0.962742176 t = -1.146270591 + 0.962742176 Combine like terms: -1.146270591 + 0.962742176 = -0.183528415 t = -0.183528415 Simplifying t = -0.183528415Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.109012767, -0.183528415}
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