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Simplifying 4.9t2 + -6t + -6 = 0 Reorder the terms: -6 + -6t + 4.9t2 = 0 Solving -6 + -6t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.224489796 + -1.224489796t + t2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + -1.224489796t + 1.224489796 + t2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + -1.224489796t + t2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + -1.224489796t + t2 = 0 + 1.224489796 -1.224489796t + t2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 -1.224489796t + t2 = 1.224489796 The t term is -1.224489796t. Take half its coefficient (-0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. -1.224489796t + 0.3748438151 + t2 = 1.224489796 + 0.3748438151 Reorder the terms: 0.3748438151 + -1.224489796t + t2 = 1.224489796 + 0.3748438151 Combine like terms: 1.224489796 + 0.3748438151 = 1.5993336111 0.3748438151 + -1.224489796t + t2 = 1.5993336111 Factor a perfect square on the left side: (t + -0.612244898)(t + -0.612244898) = 1.5993336111 Calculate the square root of the right side: 1.264647623 Break this problem into two subproblems by setting (t + -0.612244898) equal to 1.264647623 and -1.264647623.Subproblem 1
t + -0.612244898 = 1.264647623 Simplifying t + -0.612244898 = 1.264647623 Reorder the terms: -0.612244898 + t = 1.264647623 Solving -0.612244898 + t = 1.264647623 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = 1.264647623 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = 1.264647623 + 0.612244898 t = 1.264647623 + 0.612244898 Combine like terms: 1.264647623 + 0.612244898 = 1.876892521 t = 1.876892521 Simplifying t = 1.876892521Subproblem 2
t + -0.612244898 = -1.264647623 Simplifying t + -0.612244898 = -1.264647623 Reorder the terms: -0.612244898 + t = -1.264647623 Solving -0.612244898 + t = -1.264647623 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = -1.264647623 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = -1.264647623 + 0.612244898 t = -1.264647623 + 0.612244898 Combine like terms: -1.264647623 + 0.612244898 = -0.652402725 t = -0.652402725 Simplifying t = -0.652402725Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.876892521, -0.652402725}
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