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Simplifying 4t2 + 24t + 5 = 0 Reorder the terms: 5 + 24t + 4t2 = 0 Solving 5 + 24t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 6t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 6t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 6t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 6t + t2 = 0 + -1.25 6t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 6t + t2 = -1.25 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 = -1.25 + 9 Reorder the terms: 9 + 6t + t2 = -1.25 + 9 Combine like terms: -1.25 + 9 = 7.75 9 + 6t + t2 = 7.75 Factor a perfect square on the left side: (t + 3)(t + 3) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (t + 3) equal to 2.783882181 and -2.783882181.Subproblem 1
t + 3 = 2.783882181 Simplifying t + 3 = 2.783882181 Reorder the terms: 3 + t = 2.783882181 Solving 3 + t = 2.783882181 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 = 2.783882181 + -3 Combine like terms: 3 + -3 = 0 0 + t = 2.783882181 + -3 t = 2.783882181 + -3 Combine like terms: 2.783882181 + -3 = -0.216117819 t = -0.216117819 Simplifying t = -0.216117819Subproblem 2
t + 3 = -2.783882181 Simplifying t + 3 = -2.783882181 Reorder the terms: 3 + t = -2.783882181 Solving 3 + t = -2.783882181 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 = -2.783882181 + -3 Combine like terms: 3 + -3 = 0 0 + t = -2.783882181 + -3 t = -2.783882181 + -3 Combine like terms: -2.783882181 + -3 = -5.783882181 t = -5.783882181 Simplifying t = -5.783882181Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.216117819, -5.783882181}
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