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Simplifying t2 + 28t = -29 Reorder the terms: 28t + t2 = -29 Solving 28t + t2 = -29 Solving for variable 't'. Reorder the terms: 29 + 28t + t2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + 28t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 28t + -29 + t2 = 0 + -29 Reorder the terms: 29 + -29 + 28t + t2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 28t + t2 = 0 + -29 28t + t2 = 0 + -29 Combine like terms: 0 + -29 = -29 28t + t2 = -29 The t term is 28t. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28t + 196 + t2 = -29 + 196 Reorder the terms: 196 + 28t + t2 = -29 + 196 Combine like terms: -29 + 196 = 167 196 + 28t + t2 = 167 Factor a perfect square on the left side: (t + 14)(t + 14) = 167 Calculate the square root of the right side: 12.922847983 Break this problem into two subproblems by setting (t + 14) equal to 12.922847983 and -12.922847983.Subproblem 1
t + 14 = 12.922847983 Simplifying t + 14 = 12.922847983 Reorder the terms: 14 + t = 12.922847983 Solving 14 + t = 12.922847983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + t = 12.922847983 + -14 Combine like terms: 14 + -14 = 0 0 + t = 12.922847983 + -14 t = 12.922847983 + -14 Combine like terms: 12.922847983 + -14 = -1.077152017 t = -1.077152017 Simplifying t = -1.077152017Subproblem 2
t + 14 = -12.922847983 Simplifying t + 14 = -12.922847983 Reorder the terms: 14 + t = -12.922847983 Solving 14 + t = -12.922847983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + t = -12.922847983 + -14 Combine like terms: 14 + -14 = 0 0 + t = -12.922847983 + -14 t = -12.922847983 + -14 Combine like terms: -12.922847983 + -14 = -26.922847983 t = -26.922847983 Simplifying t = -26.922847983Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.077152017, -26.922847983}
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