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Simplifying 3t2 + 18t + -4 = 0 Reorder the terms: -4 + 18t + 3t2 = 0 Solving -4 + 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'. -1.333333333 + 6t + t2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 6t + 1.333333333 + t2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 6t + t2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 6t + t2 = 0 + 1.333333333 6t + t2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 6t + t2 = 1.333333333 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 = 1.333333333 + 9 Reorder the terms: 9 + 6t + t2 = 1.333333333 + 9 Combine like terms: 1.333333333 + 9 = 10.333333333 9 + 6t + t2 = 10.333333333 Factor a perfect square on the left side: (t + 3)(t + 3) = 10.333333333 Calculate the square root of the right side: 3.214550254 Break this problem into two subproblems by setting (t + 3) equal to 3.214550254 and -3.214550254.Subproblem 1
t + 3 = 3.214550254 Simplifying t + 3 = 3.214550254 Reorder the terms: 3 + t = 3.214550254 Solving 3 + t = 3.214550254 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 = 3.214550254 + -3 Combine like terms: 3 + -3 = 0 0 + t = 3.214550254 + -3 t = 3.214550254 + -3 Combine like terms: 3.214550254 + -3 = 0.214550254 t = 0.214550254 Simplifying t = 0.214550254Subproblem 2
t + 3 = -3.214550254 Simplifying t + 3 = -3.214550254 Reorder the terms: 3 + t = -3.214550254 Solving 3 + t = -3.214550254 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 = -3.214550254 + -3 Combine like terms: 3 + -3 = 0 0 + t = -3.214550254 + -3 t = -3.214550254 + -3 Combine like terms: -3.214550254 + -3 = -6.214550254 t = -6.214550254 Simplifying t = -6.214550254Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.214550254, -6.214550254}
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