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Simplifying t2 + -18.37t + -30.6 = 0 Reorder the terms: -30.6 + -18.37t + t2 = 0 Solving -30.6 + -18.37t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '30.6' to each side of the equation. -30.6 + -18.37t + 30.6 + t2 = 0 + 30.6 Reorder the terms: -30.6 + 30.6 + -18.37t + t2 = 0 + 30.6 Combine like terms: -30.6 + 30.6 = 0.0 0.0 + -18.37t + t2 = 0 + 30.6 -18.37t + t2 = 0 + 30.6 Combine like terms: 0 + 30.6 = 30.6 -18.37t + t2 = 30.6 The t term is -18.37t. Take half its coefficient (-9.185). Square it (84.364225) and add it to both sides. Add '84.364225' to each side of the equation. -18.37t + 84.364225 + t2 = 30.6 + 84.364225 Reorder the terms: 84.364225 + -18.37t + t2 = 30.6 + 84.364225 Combine like terms: 30.6 + 84.364225 = 114.964225 84.364225 + -18.37t + t2 = 114.964225 Factor a perfect square on the left side: (t + -9.185)(t + -9.185) = 114.964225 Calculate the square root of the right side: 10.722137147 Break this problem into two subproblems by setting (t + -9.185) equal to 10.722137147 and -10.722137147.Subproblem 1
t + -9.185 = 10.722137147 Simplifying t + -9.185 = 10.722137147 Reorder the terms: -9.185 + t = 10.722137147 Solving -9.185 + t = 10.722137147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.185' to each side of the equation. -9.185 + 9.185 + t = 10.722137147 + 9.185 Combine like terms: -9.185 + 9.185 = 0.000 0.000 + t = 10.722137147 + 9.185 t = 10.722137147 + 9.185 Combine like terms: 10.722137147 + 9.185 = 19.907137147 t = 19.907137147 Simplifying t = 19.907137147Subproblem 2
t + -9.185 = -10.722137147 Simplifying t + -9.185 = -10.722137147 Reorder the terms: -9.185 + t = -10.722137147 Solving -9.185 + t = -10.722137147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.185' to each side of the equation. -9.185 + 9.185 + t = -10.722137147 + 9.185 Combine like terms: -9.185 + 9.185 = 0.000 0.000 + t = -10.722137147 + 9.185 t = -10.722137147 + 9.185 Combine like terms: -10.722137147 + 9.185 = -1.537137147 t = -1.537137147 Simplifying t = -1.537137147Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.907137147, -1.537137147}
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