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Simplifying t2 + 30t + -3675 = 0 Reorder the terms: -3675 + 30t + t2 = 0 Solving -3675 + 30t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '3675' to each side of the equation. -3675 + 30t + 3675 + t2 = 0 + 3675 Reorder the terms: -3675 + 3675 + 30t + t2 = 0 + 3675 Combine like terms: -3675 + 3675 = 0 0 + 30t + t2 = 0 + 3675 30t + t2 = 0 + 3675 Combine like terms: 0 + 3675 = 3675 30t + t2 = 3675 The t term is 30t. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30t + 225 + t2 = 3675 + 225 Reorder the terms: 225 + 30t + t2 = 3675 + 225 Combine like terms: 3675 + 225 = 3900 225 + 30t + t2 = 3900 Factor a perfect square on the left side: (t + 15)(t + 15) = 3900 Calculate the square root of the right side: 62.449979984 Break this problem into two subproblems by setting (t + 15) equal to 62.449979984 and -62.449979984.Subproblem 1
t + 15 = 62.449979984 Simplifying t + 15 = 62.449979984 Reorder the terms: 15 + t = 62.449979984 Solving 15 + t = 62.449979984 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + t = 62.449979984 + -15 Combine like terms: 15 + -15 = 0 0 + t = 62.449979984 + -15 t = 62.449979984 + -15 Combine like terms: 62.449979984 + -15 = 47.449979984 t = 47.449979984 Simplifying t = 47.449979984Subproblem 2
t + 15 = -62.449979984 Simplifying t + 15 = -62.449979984 Reorder the terms: 15 + t = -62.449979984 Solving 15 + t = -62.449979984 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + t = -62.449979984 + -15 Combine like terms: 15 + -15 = 0 0 + t = -62.449979984 + -15 t = -62.449979984 + -15 Combine like terms: -62.449979984 + -15 = -77.449979984 t = -77.449979984 Simplifying t = -77.449979984Solution
The solution to the problem is based on the solutions from the subproblems. t = {47.449979984, -77.449979984}
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