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Simplifying 0 = 1 + 30t + -5t2 Solving 0 = 1 + 30t + -5t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -30t + 5t2 = 1 + 30t + -5t2 + -1 + -30t + 5t2 Reorder the terms: -1 + -30t + 5t2 = 1 + -1 + 30t + -30t + -5t2 + 5t2 Combine like terms: 1 + -1 = 0 -1 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2 -1 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2 Combine like terms: 30t + -30t = 0 -1 + -30t + 5t2 = 0 + -5t2 + 5t2 -1 + -30t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -1 + -30t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -6t + t2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -6t + 0.2 + t2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -6t + t2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -6t + t2 = 0 + 0.2 -6t + t2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -6t + t2 = 0.2 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 0.2 + 9 Reorder the terms: 9 + -6t + t2 = 0.2 + 9 Combine like terms: 0.2 + 9 = 9.2 9 + -6t + t2 = 9.2 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.2 Calculate the square root of the right side: 3.033150178 Break this problem into two subproblems by setting (t + -3) equal to 3.033150178 and -3.033150178.Subproblem 1
t + -3 = 3.033150178 Simplifying t + -3 = 3.033150178 Reorder the terms: -3 + t = 3.033150178 Solving -3 + t = 3.033150178 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.033150178 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.033150178 + 3 t = 3.033150178 + 3 Combine like terms: 3.033150178 + 3 = 6.033150178 t = 6.033150178 Simplifying t = 6.033150178Subproblem 2
t + -3 = -3.033150178 Simplifying t + -3 = -3.033150178 Reorder the terms: -3 + t = -3.033150178 Solving -3 + t = -3.033150178 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.033150178 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.033150178 + 3 t = -3.033150178 + 3 Combine like terms: -3.033150178 + 3 = -0.033150178 t = -0.033150178 Simplifying t = -0.033150178Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.033150178, -0.033150178}
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