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Simplifying -2t2 + 6t + 9 = 0 Reorder the terms: 9 + 6t + -2t2 = 0 Solving 9 + 6t + -2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -3t + t2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -3t + 4.5 + t2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -3t + t2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -3t + t2 = 0 + 4.5 -3t + t2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -3t + t2 = 4.5 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 = 4.5 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 4.5 + 2.25 Combine like terms: 4.5 + 2.25 = 6.75 2.25 + -3t + t2 = 6.75 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (t + -1.5) equal to 2.598076211 and -2.598076211.Subproblem 1
t + -1.5 = 2.598076211 Simplifying t + -1.5 = 2.598076211 Reorder the terms: -1.5 + t = 2.598076211 Solving -1.5 + t = 2.598076211 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 = 2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 2.598076211 + 1.5 t = 2.598076211 + 1.5 Combine like terms: 2.598076211 + 1.5 = 4.098076211 t = 4.098076211 Simplifying t = 4.098076211Subproblem 2
t + -1.5 = -2.598076211 Simplifying t + -1.5 = -2.598076211 Reorder the terms: -1.5 + t = -2.598076211 Solving -1.5 + t = -2.598076211 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 = -2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -2.598076211 + 1.5 t = -2.598076211 + 1.5 Combine like terms: -2.598076211 + 1.5 = -1.098076211 t = -1.098076211 Simplifying t = -1.098076211Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.098076211, -1.098076211}
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