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Simplifying -5t2 + 18t + 1.8 = 0 Reorder the terms: 1.8 + 18t + -5t2 = 0 Solving 1.8 + 18t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.36 + -3.6t + t2 = 0 Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + -3.6t + 0.36 + t2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + -3.6t + t2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + -3.6t + t2 = 0 + 0.36 -3.6t + t2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 -3.6t + t2 = 0.36 The t term is -3.6t. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6t + 3.24 + t2 = 0.36 + 3.24 Reorder the terms: 3.24 + -3.6t + t2 = 0.36 + 3.24 Combine like terms: 0.36 + 3.24 = 3.6 3.24 + -3.6t + t2 = 3.6 Factor a perfect square on the left side: (t + -1.8)(t + -1.8) = 3.6 Calculate the square root of the right side: 1.897366596 Break this problem into two subproblems by setting (t + -1.8) equal to 1.897366596 and -1.897366596.Subproblem 1
t + -1.8 = 1.897366596 Simplifying t + -1.8 = 1.897366596 Reorder the terms: -1.8 + t = 1.897366596 Solving -1.8 + t = 1.897366596 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + t = 1.897366596 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + t = 1.897366596 + 1.8 t = 1.897366596 + 1.8 Combine like terms: 1.897366596 + 1.8 = 3.697366596 t = 3.697366596 Simplifying t = 3.697366596Subproblem 2
t + -1.8 = -1.897366596 Simplifying t + -1.8 = -1.897366596 Reorder the terms: -1.8 + t = -1.897366596 Solving -1.8 + t = -1.897366596 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + t = -1.897366596 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + t = -1.897366596 + 1.8 t = -1.897366596 + 1.8 Combine like terms: -1.897366596 + 1.8 = -0.097366596 t = -0.097366596 Simplifying t = -0.097366596Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.697366596, -0.097366596}
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