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Simplifying 6t2 + -5t + -12 = 0 Reorder the terms: -12 + -5t + 6t2 = 0 Solving -12 + -5t + 6t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2 + -0.8333333333t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.8333333333t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -0.8333333333t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.8333333333t + t2 = 0 + 2 -0.8333333333t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.8333333333t + t2 = 2 The t term is -0.8333333333t. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333t + 0.1736111111 + t2 = 2 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333t + t2 = 2 + 0.1736111111 Combine like terms: 2 + 0.1736111111 = 2.1736111111 0.1736111111 + -0.8333333333t + t2 = 2.1736111111 Factor a perfect square on the left side: (t + -0.4166666667)(t + -0.4166666667) = 2.1736111111 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (t + -0.4166666667) equal to 1.474317168 and -1.474317168.Subproblem 1
t + -0.4166666667 = 1.474317168 Simplifying t + -0.4166666667 = 1.474317168 Reorder the terms: -0.4166666667 + t = 1.474317168 Solving -0.4166666667 + t = 1.474317168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + t = 1.474317168 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + t = 1.474317168 + 0.4166666667 t = 1.474317168 + 0.4166666667 Combine like terms: 1.474317168 + 0.4166666667 = 1.8909838347 t = 1.8909838347 Simplifying t = 1.8909838347Subproblem 2
t + -0.4166666667 = -1.474317168 Simplifying t + -0.4166666667 = -1.474317168 Reorder the terms: -0.4166666667 + t = -1.474317168 Solving -0.4166666667 + t = -1.474317168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + t = -1.474317168 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + t = -1.474317168 + 0.4166666667 t = -1.474317168 + 0.4166666667 Combine like terms: -1.474317168 + 0.4166666667 = -1.0576505013 t = -1.0576505013 Simplifying t = -1.0576505013Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8909838347, -1.0576505013}
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