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Simplifying 1.5t2 + -45t + -45 = 0 Reorder the terms: -45 + -45t + 1.5t2 = 0 Solving -45 + -45t + 1.5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -30 + -30t + t2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -30t + 30 + t2 = 0 + 30 Reorder the terms: -30 + 30 + -30t + t2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -30t + t2 = 0 + 30 -30t + t2 = 0 + 30 Combine like terms: 0 + 30 = 30 -30t + t2 = 30 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 = 30 + 225 Reorder the terms: 225 + -30t + t2 = 30 + 225 Combine like terms: 30 + 225 = 255 225 + -30t + t2 = 255 Factor a perfect square on the left side: (t + -15)(t + -15) = 255 Calculate the square root of the right side: 15.968719423 Break this problem into two subproblems by setting (t + -15) equal to 15.968719423 and -15.968719423.Subproblem 1
t + -15 = 15.968719423 Simplifying t + -15 = 15.968719423 Reorder the terms: -15 + t = 15.968719423 Solving -15 + t = 15.968719423 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 = 15.968719423 + 15 Combine like terms: -15 + 15 = 0 0 + t = 15.968719423 + 15 t = 15.968719423 + 15 Combine like terms: 15.968719423 + 15 = 30.968719423 t = 30.968719423 Simplifying t = 30.968719423Subproblem 2
t + -15 = -15.968719423 Simplifying t + -15 = -15.968719423 Reorder the terms: -15 + t = -15.968719423 Solving -15 + t = -15.968719423 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 = -15.968719423 + 15 Combine like terms: -15 + 15 = 0 0 + t = -15.968719423 + 15 t = -15.968719423 + 15 Combine like terms: -15.968719423 + 15 = -0.968719423 t = -0.968719423 Simplifying t = -0.968719423Solution
The solution to the problem is based on the solutions from the subproblems. t = {30.968719423, -0.968719423}
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