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Simplifying 4.9t2 + -12t + -3 = 0 Reorder the terms: -3 + -12t + 4.9t2 = 0 Solving -3 + -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'. -0.612244898 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -2.448979592t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -2.448979592t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -2.448979592t + t2 = 0 + 0.612244898 -2.448979592t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -2.448979592t + t2 = 0.612244898 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 = 0.612244898 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 0.612244898 + 1.499375261 Combine like terms: 0.612244898 + 1.499375261 = 2.111620159 1.499375261 + -2.448979592t + t2 = 2.111620159 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 2.111620159 Calculate the square root of the right side: 1.453141479 Break this problem into two subproblems by setting (t + -1.224489796) equal to 1.453141479 and -1.453141479.Subproblem 1
t + -1.224489796 = 1.453141479 Simplifying t + -1.224489796 = 1.453141479 Reorder the terms: -1.224489796 + t = 1.453141479 Solving -1.224489796 + t = 1.453141479 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 = 1.453141479 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 1.453141479 + 1.224489796 t = 1.453141479 + 1.224489796 Combine like terms: 1.453141479 + 1.224489796 = 2.677631275 t = 2.677631275 Simplifying t = 2.677631275Subproblem 2
t + -1.224489796 = -1.453141479 Simplifying t + -1.224489796 = -1.453141479 Reorder the terms: -1.224489796 + t = -1.453141479 Solving -1.224489796 + t = -1.453141479 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 = -1.453141479 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -1.453141479 + 1.224489796 t = -1.453141479 + 1.224489796 Combine like terms: -1.453141479 + 1.224489796 = -0.228651683 t = -0.228651683 Simplifying t = -0.228651683Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.677631275, -0.228651683}
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