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Simplifying 28 = t2 + -1t Reorder the terms: 28 = -1t + t2 Solving 28 = -1t + t2 Solving for variable 't'. Reorder the terms: 28 + t + -1t2 = -1t + t + t2 + -1t2 Combine like terms: -1t + t = 0 28 + t + -1t2 = 0 + t2 + -1t2 28 + t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 28 + t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + -1t + t2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -1t + 28 + t2 = 0 + 28 Reorder the terms: -28 + 28 + -1t + t2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -1t + t2 = 0 + 28 -1t + t2 = 0 + 28 Combine like terms: 0 + 28 = 28 -1t + t2 = 28 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 28 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 28 + 0.25 Combine like terms: 28 + 0.25 = 28.25 0.25 + -1t + t2 = 28.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (t + 0.5) equal to 5.315072906 and -5.315072906.Subproblem 1
t + 0.5 = 5.315072906 Simplifying t + 0.5 = 5.315072906 Reorder the terms: 0.5 + t = 5.315072906 Solving 0.5 + t = 5.315072906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 5.315072906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 5.315072906 + -0.5 t = 5.315072906 + -0.5 Combine like terms: 5.315072906 + -0.5 = 4.815072906 t = 4.815072906 Simplifying t = 4.815072906Subproblem 2
t + 0.5 = -5.315072906 Simplifying t + 0.5 = -5.315072906 Reorder the terms: 0.5 + t = -5.315072906 Solving 0.5 + t = -5.315072906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -5.315072906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -5.315072906 + -0.5 t = -5.315072906 + -0.5 Combine like terms: -5.315072906 + -0.5 = -5.815072906 t = -5.815072906 Simplifying t = -5.815072906Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.815072906, -5.815072906}
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