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Simplifying -8t2 + 71t + 192 = 0 Reorder the terms: 192 + 71t + -8t2 = 0 Solving 192 + 71t + -8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -24 + -8.875t + t2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -8.875t + 24 + t2 = 0 + 24 Reorder the terms: -24 + 24 + -8.875t + t2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -8.875t + t2 = 0 + 24 -8.875t + t2 = 0 + 24 Combine like terms: 0 + 24 = 24 -8.875t + t2 = 24 The t term is -8.875t. Take half its coefficient (-4.4375). Square it (19.69140625) and add it to both sides. Add '19.69140625' to each side of the equation. -8.875t + 19.69140625 + t2 = 24 + 19.69140625 Reorder the terms: 19.69140625 + -8.875t + t2 = 24 + 19.69140625 Combine like terms: 24 + 19.69140625 = 43.69140625 19.69140625 + -8.875t + t2 = 43.69140625 Factor a perfect square on the left side: (t + -4.4375)(t + -4.4375) = 43.69140625 Calculate the square root of the right side: 6.609947522 Break this problem into two subproblems by setting (t + -4.4375) equal to 6.609947522 and -6.609947522.Subproblem 1
t + -4.4375 = 6.609947522 Simplifying t + -4.4375 = 6.609947522 Reorder the terms: -4.4375 + t = 6.609947522 Solving -4.4375 + t = 6.609947522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.4375' to each side of the equation. -4.4375 + 4.4375 + t = 6.609947522 + 4.4375 Combine like terms: -4.4375 + 4.4375 = 0.0000 0.0000 + t = 6.609947522 + 4.4375 t = 6.609947522 + 4.4375 Combine like terms: 6.609947522 + 4.4375 = 11.047447522 t = 11.047447522 Simplifying t = 11.047447522Subproblem 2
t + -4.4375 = -6.609947522 Simplifying t + -4.4375 = -6.609947522 Reorder the terms: -4.4375 + t = -6.609947522 Solving -4.4375 + t = -6.609947522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.4375' to each side of the equation. -4.4375 + 4.4375 + t = -6.609947522 + 4.4375 Combine like terms: -4.4375 + 4.4375 = 0.0000 0.0000 + t = -6.609947522 + 4.4375 t = -6.609947522 + 4.4375 Combine like terms: -6.609947522 + 4.4375 = -2.172447522 t = -2.172447522 Simplifying t = -2.172447522Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.047447522, -2.172447522}
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