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Simplifying 250 = 40t + -0.8t2 Solving 250 = 40t + -0.8t2 Solving for variable 't'. Reorder the terms: 250 + -40t + 0.8t2 = 40t + -40t + -0.8t2 + 0.8t2 Combine like terms: 40t + -40t = 0 250 + -40t + 0.8t2 = 0 + -0.8t2 + 0.8t2 250 + -40t + 0.8t2 = -0.8t2 + 0.8t2 Combine like terms: -0.8t2 + 0.8t2 = 0.0 250 + -40t + 0.8t2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 312.5 + -50t + t2 = 0 Move the constant term to the right: Add '-312.5' to each side of the equation. 312.5 + -50t + -312.5 + t2 = 0 + -312.5 Reorder the terms: 312.5 + -312.5 + -50t + t2 = 0 + -312.5 Combine like terms: 312.5 + -312.5 = 0.0 0.0 + -50t + t2 = 0 + -312.5 -50t + t2 = 0 + -312.5 Combine like terms: 0 + -312.5 = -312.5 -50t + t2 = -312.5 The t term is -50t. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50t + 625 + t2 = -312.5 + 625 Reorder the terms: 625 + -50t + t2 = -312.5 + 625 Combine like terms: -312.5 + 625 = 312.5 625 + -50t + t2 = 312.5 Factor a perfect square on the left side: (t + -25)(t + -25) = 312.5 Calculate the square root of the right side: 17.67766953 Break this problem into two subproblems by setting (t + -25) equal to 17.67766953 and -17.67766953.Subproblem 1
t + -25 = 17.67766953 Simplifying t + -25 = 17.67766953 Reorder the terms: -25 + t = 17.67766953 Solving -25 + t = 17.67766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = 17.67766953 + 25 Combine like terms: -25 + 25 = 0 0 + t = 17.67766953 + 25 t = 17.67766953 + 25 Combine like terms: 17.67766953 + 25 = 42.67766953 t = 42.67766953 Simplifying t = 42.67766953Subproblem 2
t + -25 = -17.67766953 Simplifying t + -25 = -17.67766953 Reorder the terms: -25 + t = -17.67766953 Solving -25 + t = -17.67766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = -17.67766953 + 25 Combine like terms: -25 + 25 = 0 0 + t = -17.67766953 + 25 t = -17.67766953 + 25 Combine like terms: -17.67766953 + 25 = 7.32233047 t = 7.32233047 Simplifying t = 7.32233047Solution
The solution to the problem is based on the solutions from the subproblems. t = {42.67766953, 7.32233047}
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