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Simplifying 3t2 + -18t + -25 = 0 Reorder the terms: -25 + -18t + 3t2 = 0 Solving -25 + -18t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.333333333 + -6t + t2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + -6t + 8.333333333 + t2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + -6t + t2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + -6t + t2 = 0 + 8.333333333 -6t + t2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 -6t + t2 = 8.333333333 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 = 8.333333333 + 9 Reorder the terms: 9 + -6t + t2 = 8.333333333 + 9 Combine like terms: 8.333333333 + 9 = 17.333333333 9 + -6t + t2 = 17.333333333 Factor a perfect square on the left side: (t + -3)(t + -3) = 17.333333333 Calculate the square root of the right side: 4.163331999 Break this problem into two subproblems by setting (t + -3) equal to 4.163331999 and -4.163331999.Subproblem 1
t + -3 = 4.163331999 Simplifying t + -3 = 4.163331999 Reorder the terms: -3 + t = 4.163331999 Solving -3 + t = 4.163331999 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 = 4.163331999 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.163331999 + 3 t = 4.163331999 + 3 Combine like terms: 4.163331999 + 3 = 7.163331999 t = 7.163331999 Simplifying t = 7.163331999Subproblem 2
t + -3 = -4.163331999 Simplifying t + -3 = -4.163331999 Reorder the terms: -3 + t = -4.163331999 Solving -3 + t = -4.163331999 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 = -4.163331999 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.163331999 + 3 t = -4.163331999 + 3 Combine like terms: -4.163331999 + 3 = -1.163331999 t = -1.163331999 Simplifying t = -1.163331999Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.163331999, -1.163331999}
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