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Simplifying 1200 + -45t + 0.2t2 = 0 Solving 1200 + -45t + 0.2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 6000 + -225t + t2 = 0 Move the constant term to the right: Add '-6000' to each side of the equation. 6000 + -225t + -6000 + t2 = 0 + -6000 Reorder the terms: 6000 + -6000 + -225t + t2 = 0 + -6000 Combine like terms: 6000 + -6000 = 0 0 + -225t + t2 = 0 + -6000 -225t + t2 = 0 + -6000 Combine like terms: 0 + -6000 = -6000 -225t + t2 = -6000 The t term is -225t. Take half its coefficient (-112.5). Square it (12656.25) and add it to both sides. Add '12656.25' to each side of the equation. -225t + 12656.25 + t2 = -6000 + 12656.25 Reorder the terms: 12656.25 + -225t + t2 = -6000 + 12656.25 Combine like terms: -6000 + 12656.25 = 6656.25 12656.25 + -225t + t2 = 6656.25 Factor a perfect square on the left side: (t + -112.5)(t + -112.5) = 6656.25 Calculate the square root of the right side: 81.58584436 Break this problem into two subproblems by setting (t + -112.5) equal to 81.58584436 and -81.58584436.Subproblem 1
t + -112.5 = 81.58584436 Simplifying t + -112.5 = 81.58584436 Reorder the terms: -112.5 + t = 81.58584436 Solving -112.5 + t = 81.58584436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '112.5' to each side of the equation. -112.5 + 112.5 + t = 81.58584436 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + t = 81.58584436 + 112.5 t = 81.58584436 + 112.5 Combine like terms: 81.58584436 + 112.5 = 194.08584436 t = 194.08584436 Simplifying t = 194.08584436Subproblem 2
t + -112.5 = -81.58584436 Simplifying t + -112.5 = -81.58584436 Reorder the terms: -112.5 + t = -81.58584436 Solving -112.5 + t = -81.58584436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '112.5' to each side of the equation. -112.5 + 112.5 + t = -81.58584436 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + t = -81.58584436 + 112.5 t = -81.58584436 + 112.5 Combine like terms: -81.58584436 + 112.5 = 30.91415564 t = 30.91415564 Simplifying t = 30.91415564Solution
The solution to the problem is based on the solutions from the subproblems. t = {194.08584436, 30.91415564}
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