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Simplifying 4.9(t2) + -12t + -55 = 0 Reorder the terms: -55 + -12t + 4.9t2 = 0 Solving -55 + -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'. -11.2244898 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '11.2244898' to each side of the equation. -11.2244898 + -2.448979592t + 11.2244898 + t2 = 0 + 11.2244898 Reorder the terms: -11.2244898 + 11.2244898 + -2.448979592t + t2 = 0 + 11.2244898 Combine like terms: -11.2244898 + 11.2244898 = 0.0000000 0.0000000 + -2.448979592t + t2 = 0 + 11.2244898 -2.448979592t + t2 = 0 + 11.2244898 Combine like terms: 0 + 11.2244898 = 11.2244898 -2.448979592t + t2 = 11.2244898 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 = 11.2244898 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 11.2244898 + 1.499375261 Combine like terms: 11.2244898 + 1.499375261 = 12.723865061 1.499375261 + -2.448979592t + t2 = 12.723865061 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 12.723865061 Calculate the square root of the right side: 3.567052714 Break this problem into two subproblems by setting (t + -1.224489796) equal to 3.567052714 and -3.567052714.Subproblem 1
t + -1.224489796 = 3.567052714 Simplifying t + -1.224489796 = 3.567052714 Reorder the terms: -1.224489796 + t = 3.567052714 Solving -1.224489796 + t = 3.567052714 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 = 3.567052714 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 3.567052714 + 1.224489796 t = 3.567052714 + 1.224489796 Combine like terms: 3.567052714 + 1.224489796 = 4.79154251 t = 4.79154251 Simplifying t = 4.79154251Subproblem 2
t + -1.224489796 = -3.567052714 Simplifying t + -1.224489796 = -3.567052714 Reorder the terms: -1.224489796 + t = -3.567052714 Solving -1.224489796 + t = -3.567052714 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 = -3.567052714 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -3.567052714 + 1.224489796 t = -3.567052714 + 1.224489796 Combine like terms: -3.567052714 + 1.224489796 = -2.342562918 t = -2.342562918 Simplifying t = -2.342562918Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.79154251, -2.342562918}
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