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Simplifying -4.9t2 + 30.5t + 9.8 = 0 Reorder the terms: 9.8 + 30.5t + -4.9t2 = 0 Solving 9.8 + 30.5t + -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'. -2 + -6.224489796t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6.224489796t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -6.224489796t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6.224489796t + t2 = 0 + 2 -6.224489796t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6.224489796t + t2 = 2 The t term is -6.224489796t. Take half its coefficient (-3.112244898). Square it (9.686068305) and add it to both sides. Add '9.686068305' to each side of the equation. -6.224489796t + 9.686068305 + t2 = 2 + 9.686068305 Reorder the terms: 9.686068305 + -6.224489796t + t2 = 2 + 9.686068305 Combine like terms: 2 + 9.686068305 = 11.686068305 9.686068305 + -6.224489796t + t2 = 11.686068305 Factor a perfect square on the left side: (t + -3.112244898)(t + -3.112244898) = 11.686068305 Calculate the square root of the right side: 3.418489185 Break this problem into two subproblems by setting (t + -3.112244898) equal to 3.418489185 and -3.418489185.Subproblem 1
t + -3.112244898 = 3.418489185 Simplifying t + -3.112244898 = 3.418489185 Reorder the terms: -3.112244898 + t = 3.418489185 Solving -3.112244898 + t = 3.418489185 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + t = 3.418489185 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + t = 3.418489185 + 3.112244898 t = 3.418489185 + 3.112244898 Combine like terms: 3.418489185 + 3.112244898 = 6.530734083 t = 6.530734083 Simplifying t = 6.530734083Subproblem 2
t + -3.112244898 = -3.418489185 Simplifying t + -3.112244898 = -3.418489185 Reorder the terms: -3.112244898 + t = -3.418489185 Solving -3.112244898 + t = -3.418489185 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + t = -3.418489185 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + t = -3.418489185 + 3.112244898 t = -3.418489185 + 3.112244898 Combine like terms: -3.418489185 + 3.112244898 = -0.306244287 t = -0.306244287 Simplifying t = -0.306244287Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.530734083, -0.306244287}
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