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Simplifying 0 = 0.1t2 + -3.5t + 6 Reorder the terms: 0 = 6 + -3.5t + 0.1t2 Solving 0 = 6 + -3.5t + 0.1t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + 3.5t + -0.1t2 = 6 + -3.5t + 0.1t2 + -6 + 3.5t + -0.1t2 Reorder the terms: -6 + 3.5t + -0.1t2 = 6 + -6 + -3.5t + 3.5t + 0.1t2 + -0.1t2 Combine like terms: 6 + -6 = 0 -6 + 3.5t + -0.1t2 = 0 + -3.5t + 3.5t + 0.1t2 + -0.1t2 -6 + 3.5t + -0.1t2 = -3.5t + 3.5t + 0.1t2 + -0.1t2 Combine like terms: -3.5t + 3.5t = 0.0 -6 + 3.5t + -0.1t2 = 0.0 + 0.1t2 + -0.1t2 -6 + 3.5t + -0.1t2 = 0.1t2 + -0.1t2 Combine like terms: 0.1t2 + -0.1t2 = 0.0 -6 + 3.5t + -0.1t2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 60 + -35t + t2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -35t + -60 + t2 = 0 + -60 Reorder the terms: 60 + -60 + -35t + t2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -35t + t2 = 0 + -60 -35t + t2 = 0 + -60 Combine like terms: 0 + -60 = -60 -35t + t2 = -60 The t term is -35t. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35t + 306.25 + t2 = -60 + 306.25 Reorder the terms: 306.25 + -35t + t2 = -60 + 306.25 Combine like terms: -60 + 306.25 = 246.25 306.25 + -35t + t2 = 246.25 Factor a perfect square on the left side: (t + -17.5)(t + -17.5) = 246.25 Calculate the square root of the right side: 15.692354826 Break this problem into two subproblems by setting (t + -17.5) equal to 15.692354826 and -15.692354826.Subproblem 1
t + -17.5 = 15.692354826 Simplifying t + -17.5 = 15.692354826 Reorder the terms: -17.5 + t = 15.692354826 Solving -17.5 + t = 15.692354826 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + t = 15.692354826 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + t = 15.692354826 + 17.5 t = 15.692354826 + 17.5 Combine like terms: 15.692354826 + 17.5 = 33.192354826 t = 33.192354826 Simplifying t = 33.192354826Subproblem 2
t + -17.5 = -15.692354826 Simplifying t + -17.5 = -15.692354826 Reorder the terms: -17.5 + t = -15.692354826 Solving -17.5 + t = -15.692354826 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + t = -15.692354826 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + t = -15.692354826 + 17.5 t = -15.692354826 + 17.5 Combine like terms: -15.692354826 + 17.5 = 1.807645174 t = 1.807645174 Simplifying t = 1.807645174Solution
The solution to the problem is based on the solutions from the subproblems. t = {33.192354826, 1.807645174}
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