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Simplifying 12t2 + 18t + 2 = 0 Reorder the terms: 2 + 18t + 12t2 = 0 Solving 2 + 18t + 12t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 9t + 6t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 9t + 6t2)' equal to zero and attempt to solve: Simplifying 1 + 9t + 6t2 = 0 Solving 1 + 9t + 6t2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 1.5t + t2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 1.5t + -0.1666666667 + t2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 1.5t + t2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 1.5t + t2 = 0 + -0.1666666667 1.5t + t2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 1.5t + t2 = -0.1666666667 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = -0.1666666667 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = -0.1666666667 + 0.5625 Combine like terms: -0.1666666667 + 0.5625 = 0.3958333333 0.5625 + 1.5t + t2 = 0.3958333333 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = 0.3958333333 Calculate the square root of the right side: 0.62915287 Break this problem into two subproblems by setting (t + 0.75) equal to 0.62915287 and -0.62915287.Subproblem 1
t + 0.75 = 0.62915287 Simplifying t + 0.75 = 0.62915287 Reorder the terms: 0.75 + t = 0.62915287 Solving 0.75 + t = 0.62915287 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = 0.62915287 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = 0.62915287 + -0.75 t = 0.62915287 + -0.75 Combine like terms: 0.62915287 + -0.75 = -0.12084713 t = -0.12084713 Simplifying t = -0.12084713Subproblem 2
t + 0.75 = -0.62915287 Simplifying t + 0.75 = -0.62915287 Reorder the terms: 0.75 + t = -0.62915287 Solving 0.75 + t = -0.62915287 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = -0.62915287 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = -0.62915287 + -0.75 t = -0.62915287 + -0.75 Combine like terms: -0.62915287 + -0.75 = -1.37915287 t = -1.37915287 Simplifying t = -1.37915287Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.12084713, -1.37915287}Solution
t = {-0.12084713, -1.37915287}
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