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Simplifying -5t2 + 30t = 24 Reorder the terms: 30t + -5t2 = 24 Solving 30t + -5t2 = 24 Solving for variable 't'. Reorder the terms: -24 + 30t + -5t2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 30t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 4.8 + -6t + t2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -6t + -4.8 + t2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -6t + t2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -6t + t2 = 0 + -4.8 -6t + t2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -6t + t2 = -4.8 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 = -4.8 + 9 Reorder the terms: 9 + -6t + t2 = -4.8 + 9 Combine like terms: -4.8 + 9 = 4.2 9 + -6t + t2 = 4.2 Factor a perfect square on the left side: (t + -3)(t + -3) = 4.2 Calculate the square root of the right side: 2.049390153 Break this problem into two subproblems by setting (t + -3) equal to 2.049390153 and -2.049390153.Subproblem 1
t + -3 = 2.049390153 Simplifying t + -3 = 2.049390153 Reorder the terms: -3 + t = 2.049390153 Solving -3 + t = 2.049390153 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 = 2.049390153 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.049390153 + 3 t = 2.049390153 + 3 Combine like terms: 2.049390153 + 3 = 5.049390153 t = 5.049390153 Simplifying t = 5.049390153Subproblem 2
t + -3 = -2.049390153 Simplifying t + -3 = -2.049390153 Reorder the terms: -3 + t = -2.049390153 Solving -3 + t = -2.049390153 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 = -2.049390153 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.049390153 + 3 t = -2.049390153 + 3 Combine like terms: -2.049390153 + 3 = 0.950609847 t = 0.950609847 Simplifying t = 0.950609847Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.049390153, 0.950609847}
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