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Simplifying -4.9t2 + 6t + 0.6 = 0 Reorder the terms: 0.6 + 6t + -4.9t2 = 0 Solving 0.6 + 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'. -0.1224489796 + -1.224489796t + t2 = 0 Move the constant term to the right: Add '0.1224489796' to each side of the equation. -0.1224489796 + -1.224489796t + 0.1224489796 + t2 = 0 + 0.1224489796 Reorder the terms: -0.1224489796 + 0.1224489796 + -1.224489796t + t2 = 0 + 0.1224489796 Combine like terms: -0.1224489796 + 0.1224489796 = 0.0000000000 0.0000000000 + -1.224489796t + t2 = 0 + 0.1224489796 -1.224489796t + t2 = 0 + 0.1224489796 Combine like terms: 0 + 0.1224489796 = 0.1224489796 -1.224489796t + t2 = 0.1224489796 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 = 0.1224489796 + 0.3748438151 Reorder the terms: 0.3748438151 + -1.224489796t + t2 = 0.1224489796 + 0.3748438151 Combine like terms: 0.1224489796 + 0.3748438151 = 0.4972927947 0.3748438151 + -1.224489796t + t2 = 0.4972927947 Factor a perfect square on the left side: (t + -0.612244898)(t + -0.612244898) = 0.4972927947 Calculate the square root of the right side: 0.7051899 Break this problem into two subproblems by setting (t + -0.612244898) equal to 0.7051899 and -0.7051899.Subproblem 1
t + -0.612244898 = 0.7051899 Simplifying t + -0.612244898 = 0.7051899 Reorder the terms: -0.612244898 + t = 0.7051899 Solving -0.612244898 + t = 0.7051899 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 = 0.7051899 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = 0.7051899 + 0.612244898 t = 0.7051899 + 0.612244898 Combine like terms: 0.7051899 + 0.612244898 = 1.317434798 t = 1.317434798 Simplifying t = 1.317434798Subproblem 2
t + -0.612244898 = -0.7051899 Simplifying t + -0.612244898 = -0.7051899 Reorder the terms: -0.612244898 + t = -0.7051899 Solving -0.612244898 + t = -0.7051899 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 = -0.7051899 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = -0.7051899 + 0.612244898 t = -0.7051899 + 0.612244898 Combine like terms: -0.7051899 + 0.612244898 = -0.092945002 t = -0.092945002 Simplifying t = -0.092945002Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.317434798, -0.092945002}
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