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Simplifying 1.8t + -0.03t2 + -22 = 0 Reorder the terms: -22 + 1.8t + -0.03t2 = 0 Solving -22 + 1.8t + -0.03t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. 733.3333333 + -60t + t2 = 0 Move the constant term to the right: Add '-733.3333333' to each side of the equation. 733.3333333 + -60t + -733.3333333 + t2 = 0 + -733.3333333 Reorder the terms: 733.3333333 + -733.3333333 + -60t + t2 = 0 + -733.3333333 Combine like terms: 733.3333333 + -733.3333333 = 0.0000000 0.0000000 + -60t + t2 = 0 + -733.3333333 -60t + t2 = 0 + -733.3333333 Combine like terms: 0 + -733.3333333 = -733.3333333 -60t + t2 = -733.3333333 The t term is -60t. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60t + 900 + t2 = -733.3333333 + 900 Reorder the terms: 900 + -60t + t2 = -733.3333333 + 900 Combine like terms: -733.3333333 + 900 = 166.6666667 900 + -60t + t2 = 166.6666667 Factor a perfect square on the left side: (t + -30)(t + -30) = 166.6666667 Calculate the square root of the right side: 12.909944489 Break this problem into two subproblems by setting (t + -30) equal to 12.909944489 and -12.909944489.Subproblem 1
t + -30 = 12.909944489 Simplifying t + -30 = 12.909944489 Reorder the terms: -30 + t = 12.909944489 Solving -30 + t = 12.909944489 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + t = 12.909944489 + 30 Combine like terms: -30 + 30 = 0 0 + t = 12.909944489 + 30 t = 12.909944489 + 30 Combine like terms: 12.909944489 + 30 = 42.909944489 t = 42.909944489 Simplifying t = 42.909944489Subproblem 2
t + -30 = -12.909944489 Simplifying t + -30 = -12.909944489 Reorder the terms: -30 + t = -12.909944489 Solving -30 + t = -12.909944489 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + t = -12.909944489 + 30 Combine like terms: -30 + 30 = 0 0 + t = -12.909944489 + 30 t = -12.909944489 + 30 Combine like terms: -12.909944489 + 30 = 17.090055511 t = 17.090055511 Simplifying t = 17.090055511Solution
The solution to the problem is based on the solutions from the subproblems. t = {42.909944489, 17.090055511}
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