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Simplifying 4.9t2 + -12t + 5.0 = 0 Reorder the terms: 5.0 + -12t + 4.9t2 = 0 Solving 5.0 + -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'. 1.020408163 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '-1.020408163' to each side of the equation. 1.020408163 + -2.448979592t + -1.020408163 + t2 = 0 + -1.020408163 Reorder the terms: 1.020408163 + -1.020408163 + -2.448979592t + t2 = 0 + -1.020408163 Combine like terms: 1.020408163 + -1.020408163 = 0.000000000 0.000000000 + -2.448979592t + t2 = 0 + -1.020408163 -2.448979592t + t2 = 0 + -1.020408163 Combine like terms: 0 + -1.020408163 = -1.020408163 -2.448979592t + t2 = -1.020408163 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 = -1.020408163 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = -1.020408163 + 1.499375261 Combine like terms: -1.020408163 + 1.499375261 = 0.478967098 1.499375261 + -2.448979592t + t2 = 0.478967098 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 0.478967098 Calculate the square root of the right side: 0.692074489 Break this problem into two subproblems by setting (t + -1.224489796) equal to 0.692074489 and -0.692074489.Subproblem 1
t + -1.224489796 = 0.692074489 Simplifying t + -1.224489796 = 0.692074489 Reorder the terms: -1.224489796 + t = 0.692074489 Solving -1.224489796 + t = 0.692074489 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 = 0.692074489 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 0.692074489 + 1.224489796 t = 0.692074489 + 1.224489796 Combine like terms: 0.692074489 + 1.224489796 = 1.916564285 t = 1.916564285 Simplifying t = 1.916564285Subproblem 2
t + -1.224489796 = -0.692074489 Simplifying t + -1.224489796 = -0.692074489 Reorder the terms: -1.224489796 + t = -0.692074489 Solving -1.224489796 + t = -0.692074489 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 = -0.692074489 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -0.692074489 + 1.224489796 t = -0.692074489 + 1.224489796 Combine like terms: -0.692074489 + 1.224489796 = 0.532415307 t = 0.532415307 Simplifying t = 0.532415307Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.916564285, 0.532415307}
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