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Simplifying 0 = -4.9t2 + 12t + -2 Reorder the terms: 0 = -2 + 12t + -4.9t2 Solving 0 = -2 + 12t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + 2 = 2 2 + -12t + 4.9t2 = -2 + 12t + -4.9t2 + 2 + -12t + 4.9t2 Reorder the terms: 2 + -12t + 4.9t2 = -2 + 2 + 12t + -12t + -4.9t2 + 4.9t2 Combine like terms: -2 + 2 = 0 2 + -12t + 4.9t2 = 0 + 12t + -12t + -4.9t2 + 4.9t2 2 + -12t + 4.9t2 = 12t + -12t + -4.9t2 + 4.9t2 Combine like terms: 12t + -12t = 0 2 + -12t + 4.9t2 = 0 + -4.9t2 + 4.9t2 2 + -12t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 2 + -12t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.4081632653 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -2.448979592t + -0.4081632653 + t2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -2.448979592t + t2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -2.448979592t + t2 = 0 + -0.4081632653 -2.448979592t + t2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -2.448979592t + t2 = -0.4081632653 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 = -0.4081632653 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = -0.4081632653 + 1.499375261 Combine like terms: -0.4081632653 + 1.499375261 = 1.0912119957 1.499375261 + -2.448979592t + t2 = 1.0912119957 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 1.0912119957 Calculate the square root of the right side: 1.04461093 Break this problem into two subproblems by setting (t + -1.224489796) equal to 1.04461093 and -1.04461093.Subproblem 1
t + -1.224489796 = 1.04461093 Simplifying t + -1.224489796 = 1.04461093 Reorder the terms: -1.224489796 + t = 1.04461093 Solving -1.224489796 + t = 1.04461093 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 = 1.04461093 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 1.04461093 + 1.224489796 t = 1.04461093 + 1.224489796 Combine like terms: 1.04461093 + 1.224489796 = 2.269100726 t = 2.269100726 Simplifying t = 2.269100726Subproblem 2
t + -1.224489796 = -1.04461093 Simplifying t + -1.224489796 = -1.04461093 Reorder the terms: -1.224489796 + t = -1.04461093 Solving -1.224489796 + t = -1.04461093 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 = -1.04461093 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -1.04461093 + 1.224489796 t = -1.04461093 + 1.224489796 Combine like terms: -1.04461093 + 1.224489796 = 0.179878866 t = 0.179878866 Simplifying t = 0.179878866Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.269100726, 0.179878866}
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