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Simplifying 6t2 + -18t + -5 = 0 Reorder the terms: -5 + -18t + 6t2 = 0 Solving -5 + -18t + 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'. -0.8333333333 + -3t + t2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -3t + 0.8333333333 + t2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -3t + t2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -3t + t2 = 0 + 0.8333333333 -3t + t2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -3t + t2 = 0.8333333333 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 0.8333333333 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 0.8333333333 + 2.25 Combine like terms: 0.8333333333 + 2.25 = 3.0833333333 2.25 + -3t + t2 = 3.0833333333 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 3.0833333333 Calculate the square root of the right side: 1.755942292 Break this problem into two subproblems by setting (t + -1.5) equal to 1.755942292 and -1.755942292.Subproblem 1
t + -1.5 = 1.755942292 Simplifying t + -1.5 = 1.755942292 Reorder the terms: -1.5 + t = 1.755942292 Solving -1.5 + t = 1.755942292 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 1.755942292 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 1.755942292 + 1.5 t = 1.755942292 + 1.5 Combine like terms: 1.755942292 + 1.5 = 3.255942292 t = 3.255942292 Simplifying t = 3.255942292Subproblem 2
t + -1.5 = -1.755942292 Simplifying t + -1.5 = -1.755942292 Reorder the terms: -1.5 + t = -1.755942292 Solving -1.5 + t = -1.755942292 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -1.755942292 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -1.755942292 + 1.5 t = -1.755942292 + 1.5 Combine like terms: -1.755942292 + 1.5 = -0.255942292 t = -0.255942292 Simplifying t = -0.255942292Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.255942292, -0.255942292}
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