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Simplifying 5(t2) + -24.25(t) + 17 = 0 Reorder the terms: 17 + -24.25t + 5t2 = 0 Solving 17 + -24.25t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.4 + -4.85t + t2 = 0 Move the constant term to the right: Add '-3.4' to each side of the equation. 3.4 + -4.85t + -3.4 + t2 = 0 + -3.4 Reorder the terms: 3.4 + -3.4 + -4.85t + t2 = 0 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + -4.85t + t2 = 0 + -3.4 -4.85t + t2 = 0 + -3.4 Combine like terms: 0 + -3.4 = -3.4 -4.85t + t2 = -3.4 The t term is -4.85t. Take half its coefficient (-2.425). Square it (5.880625) and add it to both sides. Add '5.880625' to each side of the equation. -4.85t + 5.880625 + t2 = -3.4 + 5.880625 Reorder the terms: 5.880625 + -4.85t + t2 = -3.4 + 5.880625 Combine like terms: -3.4 + 5.880625 = 2.480625 5.880625 + -4.85t + t2 = 2.480625 Factor a perfect square on the left side: (t + -2.425)(t + -2.425) = 2.480625 Calculate the square root of the right side: 1.575 Break this problem into two subproblems by setting (t + -2.425) equal to 1.575 and -1.575.Subproblem 1
t + -2.425 = 1.575 Simplifying t + -2.425 = 1.575 Reorder the terms: -2.425 + t = 1.575 Solving -2.425 + t = 1.575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.425' to each side of the equation. -2.425 + 2.425 + t = 1.575 + 2.425 Combine like terms: -2.425 + 2.425 = 0.000 0.000 + t = 1.575 + 2.425 t = 1.575 + 2.425 Combine like terms: 1.575 + 2.425 = 4 t = 4 Simplifying t = 4Subproblem 2
t + -2.425 = -1.575 Simplifying t + -2.425 = -1.575 Reorder the terms: -2.425 + t = -1.575 Solving -2.425 + t = -1.575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.425' to each side of the equation. -2.425 + 2.425 + t = -1.575 + 2.425 Combine like terms: -2.425 + 2.425 = 0.000 0.000 + t = -1.575 + 2.425 t = -1.575 + 2.425 Combine like terms: -1.575 + 2.425 = 0.85 t = 0.85 Simplifying t = 0.85Solution
The solution to the problem is based on the solutions from the subproblems. t = {4, 0.85}
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