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Simplifying 5t2 + -25t + 24 = 0 Reorder the terms: 24 + -25t + 5t2 = 0 Solving 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'. 4.8 + -5t + t2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -5t + -4.8 + t2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -5t + t2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -5t + t2 = 0 + -4.8 -5t + t2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -5t + t2 = -4.8 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -4.8 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -4.8 + 6.25 Combine like terms: -4.8 + 6.25 = 1.45 6.25 + -5t + t2 = 1.45 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (t + -2.5) equal to 1.204159458 and -1.204159458.Subproblem 1
t + -2.5 = 1.204159458 Simplifying t + -2.5 = 1.204159458 Reorder the terms: -2.5 + t = 1.204159458 Solving -2.5 + t = 1.204159458 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 1.204159458 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 1.204159458 + 2.5 t = 1.204159458 + 2.5 Combine like terms: 1.204159458 + 2.5 = 3.704159458 t = 3.704159458 Simplifying t = 3.704159458Subproblem 2
t + -2.5 = -1.204159458 Simplifying t + -2.5 = -1.204159458 Reorder the terms: -2.5 + t = -1.204159458 Solving -2.5 + t = -1.204159458 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -1.204159458 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -1.204159458 + 2.5 t = -1.204159458 + 2.5 Combine like terms: -1.204159458 + 2.5 = 1.295840542 t = 1.295840542 Simplifying t = 1.295840542Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.704159458, 1.295840542}
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