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Simplifying -4.9t2 + 12t + 0.6 = 0 Reorder the terms: 0.6 + 12t + -4.9t2 = 0 Solving 0.6 + 12t + -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 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '0.1224489796' to each side of the equation. -0.1224489796 + -2.448979592t + 0.1224489796 + t2 = 0 + 0.1224489796 Reorder the terms: -0.1224489796 + 0.1224489796 + -2.448979592t + t2 = 0 + 0.1224489796 Combine like terms: -0.1224489796 + 0.1224489796 = 0.0000000000 0.0000000000 + -2.448979592t + t2 = 0 + 0.1224489796 -2.448979592t + t2 = 0 + 0.1224489796 Combine like terms: 0 + 0.1224489796 = 0.1224489796 -2.448979592t + t2 = 0.1224489796 The t term is -2.448979592t. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592t + 1.499375261 + t2 = 0.1224489796 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 0.1224489796 + 1.499375261 Combine like terms: 0.1224489796 + 1.499375261 = 1.6218242406 1.499375261 + -2.448979592t + t2 = 1.6218242406 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 1.6218242406 Calculate the square root of the right side: 1.273508634 Break this problem into two subproblems by setting (t + -1.224489796) equal to 1.273508634 and -1.273508634.Subproblem 1
t + -1.224489796 = 1.273508634 Simplifying t + -1.224489796 = 1.273508634 Reorder the terms: -1.224489796 + t = 1.273508634 Solving -1.224489796 + t = 1.273508634 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = 1.273508634 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 1.273508634 + 1.224489796 t = 1.273508634 + 1.224489796 Combine like terms: 1.273508634 + 1.224489796 = 2.49799843 t = 2.49799843 Simplifying t = 2.49799843Subproblem 2
t + -1.224489796 = -1.273508634 Simplifying t + -1.224489796 = -1.273508634 Reorder the terms: -1.224489796 + t = -1.273508634 Solving -1.224489796 + t = -1.273508634 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = -1.273508634 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -1.273508634 + 1.224489796 t = -1.273508634 + 1.224489796 Combine like terms: -1.273508634 + 1.224489796 = -0.049018838 t = -0.049018838 Simplifying t = -0.049018838Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.49799843, -0.049018838}
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