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Simplifying 0.83t2 + -13t + 38 = 0 Reorder the terms: 38 + -13t + 0.83t2 = 0 Solving 38 + -13t + 0.83t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.83 the coefficient of the squared term: Divide each side by '0.83'. 45.78313253 + -15.6626506t + t2 = 0 Move the constant term to the right: Add '-45.78313253' to each side of the equation. 45.78313253 + -15.6626506t + -45.78313253 + t2 = 0 + -45.78313253 Reorder the terms: 45.78313253 + -45.78313253 + -15.6626506t + t2 = 0 + -45.78313253 Combine like terms: 45.78313253 + -45.78313253 = 0.00000000 0.00000000 + -15.6626506t + t2 = 0 + -45.78313253 -15.6626506t + t2 = 0 + -45.78313253 Combine like terms: 0 + -45.78313253 = -45.78313253 -15.6626506t + t2 = -45.78313253 The t term is -15.6626506t. Take half its coefficient (-7.8313253). Square it (61.32965595) and add it to both sides. Add '61.32965595' to each side of the equation. -15.6626506t + 61.32965595 + t2 = -45.78313253 + 61.32965595 Reorder the terms: 61.32965595 + -15.6626506t + t2 = -45.78313253 + 61.32965595 Combine like terms: -45.78313253 + 61.32965595 = 15.54652342 61.32965595 + -15.6626506t + t2 = 15.54652342 Factor a perfect square on the left side: (t + -7.8313253)(t + -7.8313253) = 15.54652342 Calculate the square root of the right side: 3.94290799 Break this problem into two subproblems by setting (t + -7.8313253) equal to 3.94290799 and -3.94290799.Subproblem 1
t + -7.8313253 = 3.94290799 Simplifying t + -7.8313253 = 3.94290799 Reorder the terms: -7.8313253 + t = 3.94290799 Solving -7.8313253 + t = 3.94290799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.8313253' to each side of the equation. -7.8313253 + 7.8313253 + t = 3.94290799 + 7.8313253 Combine like terms: -7.8313253 + 7.8313253 = 0.0000000 0.0000000 + t = 3.94290799 + 7.8313253 t = 3.94290799 + 7.8313253 Combine like terms: 3.94290799 + 7.8313253 = 11.77423329 t = 11.77423329 Simplifying t = 11.77423329Subproblem 2
t + -7.8313253 = -3.94290799 Simplifying t + -7.8313253 = -3.94290799 Reorder the terms: -7.8313253 + t = -3.94290799 Solving -7.8313253 + t = -3.94290799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.8313253' to each side of the equation. -7.8313253 + 7.8313253 + t = -3.94290799 + 7.8313253 Combine like terms: -7.8313253 + 7.8313253 = 0.0000000 0.0000000 + t = -3.94290799 + 7.8313253 t = -3.94290799 + 7.8313253 Combine like terms: -3.94290799 + 7.8313253 = 3.88841731 t = 3.88841731 Simplifying t = 3.88841731Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.77423329, 3.88841731}
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