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Simplifying 0.20t2 + -45.0t = 1000 Reorder the terms: -45.0t + 0.20t2 = 1000 Solving -45.0t + 0.20t2 = 1000 Solving for variable 't'. Reorder the terms: -1000 + -45.0t + 0.20t2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + -45.0t + 0.20t2 = 0 Begin completing the square. Divide all terms by 0.20 the coefficient of the squared term: Divide each side by '0.20'. -5000 + -225t + t2 = 0 Move the constant term to the right: Add '5000' to each side of the equation. -5000 + -225t + 5000 + t2 = 0 + 5000 Reorder the terms: -5000 + 5000 + -225t + t2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + -225t + t2 = 0 + 5000 -225t + t2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 -225t + t2 = 5000 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 = 5000 + 12656.25 Reorder the terms: 12656.25 + -225t + t2 = 5000 + 12656.25 Combine like terms: 5000 + 12656.25 = 17656.25 12656.25 + -225t + t2 = 17656.25 Factor a perfect square on the left side: (t + -112.5)(t + -112.5) = 17656.25 Calculate the square root of the right side: 132.876822659 Break this problem into two subproblems by setting (t + -112.5) equal to 132.876822659 and -132.876822659.Subproblem 1
t + -112.5 = 132.876822659 Simplifying t + -112.5 = 132.876822659 Reorder the terms: -112.5 + t = 132.876822659 Solving -112.5 + t = 132.876822659 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 = 132.876822659 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + t = 132.876822659 + 112.5 t = 132.876822659 + 112.5 Combine like terms: 132.876822659 + 112.5 = 245.376822659 t = 245.376822659 Simplifying t = 245.376822659Subproblem 2
t + -112.5 = -132.876822659 Simplifying t + -112.5 = -132.876822659 Reorder the terms: -112.5 + t = -132.876822659 Solving -112.5 + t = -132.876822659 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 = -132.876822659 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + t = -132.876822659 + 112.5 t = -132.876822659 + 112.5 Combine like terms: -132.876822659 + 112.5 = -20.376822659 t = -20.376822659 Simplifying t = -20.376822659Solution
The solution to the problem is based on the solutions from the subproblems. t = {245.376822659, -20.376822659}
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