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Simplifying 0.583t2 + 4t + -12 = 0 Reorder the terms: -12 + 4t + 0.583t2 = 0 Solving -12 + 4t + 0.583t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.583 the coefficient of the squared term: Divide each side by '0.583'. -20.58319039 + 6.861063465t + t2 = 0 Move the constant term to the right: Add '20.58319039' to each side of the equation. -20.58319039 + 6.861063465t + 20.58319039 + t2 = 0 + 20.58319039 Reorder the terms: -20.58319039 + 20.58319039 + 6.861063465t + t2 = 0 + 20.58319039 Combine like terms: -20.58319039 + 20.58319039 = 0.00000000 0.00000000 + 6.861063465t + t2 = 0 + 20.58319039 6.861063465t + t2 = 0 + 20.58319039 Combine like terms: 0 + 20.58319039 = 20.58319039 6.861063465t + t2 = 20.58319039 The t term is 6.861063465t. Take half its coefficient (3.430531733). Square it (11.76854797) and add it to both sides. Add '11.76854797' to each side of the equation. 6.861063465t + 11.76854797 + t2 = 20.58319039 + 11.76854797 Reorder the terms: 11.76854797 + 6.861063465t + t2 = 20.58319039 + 11.76854797 Combine like terms: 20.58319039 + 11.76854797 = 32.35173836 11.76854797 + 6.861063465t + t2 = 32.35173836 Factor a perfect square on the left side: (t + 3.430531733)(t + 3.430531733) = 32.35173836 Calculate the square root of the right side: 5.687858855 Break this problem into two subproblems by setting (t + 3.430531733) equal to 5.687858855 and -5.687858855.Subproblem 1
t + 3.430531733 = 5.687858855 Simplifying t + 3.430531733 = 5.687858855 Reorder the terms: 3.430531733 + t = 5.687858855 Solving 3.430531733 + t = 5.687858855 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.430531733' to each side of the equation. 3.430531733 + -3.430531733 + t = 5.687858855 + -3.430531733 Combine like terms: 3.430531733 + -3.430531733 = 0.000000000 0.000000000 + t = 5.687858855 + -3.430531733 t = 5.687858855 + -3.430531733 Combine like terms: 5.687858855 + -3.430531733 = 2.257327122 t = 2.257327122 Simplifying t = 2.257327122Subproblem 2
t + 3.430531733 = -5.687858855 Simplifying t + 3.430531733 = -5.687858855 Reorder the terms: 3.430531733 + t = -5.687858855 Solving 3.430531733 + t = -5.687858855 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.430531733' to each side of the equation. 3.430531733 + -3.430531733 + t = -5.687858855 + -3.430531733 Combine like terms: 3.430531733 + -3.430531733 = 0.000000000 0.000000000 + t = -5.687858855 + -3.430531733 t = -5.687858855 + -3.430531733 Combine like terms: -5.687858855 + -3.430531733 = -9.118390588 t = -9.118390588 Simplifying t = -9.118390588Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.257327122, -9.118390588}
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