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Simplifying (0.5 * 9.8t2) + (189t) = 295 Multiply 0.5 * 9.8 (4.9t2) + (189t) = 295 Reorder the terms: (189t) + (4.9t2) = 295 Solving (189t) + (4.9t2) = 295 Solving for variable 't'. Reorder the terms: -295 + (189t) + (4.9t2) = 295 + -295 Combine like terms: 295 + -295 = 0 -295 + (189t) + (4.9t2) = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -60.20408163 + (38.57142857t) + t2 = 0 Move the constant term to the right: Add '60.20408163' to each side of the equation. -60.20408163 + (38.57142857t) + 60.20408163 + t2 = 0 + 60.20408163 Reorder the terms: -60.20408163 + 60.20408163 + (38.57142857t) + t2 = 0 + 60.20408163 Combine like terms: -60.20408163 + 60.20408163 = 0.00000000 0.00000000 + (38.57142857t) + t2 = 0 + 60.20408163 (38.57142857t) + t2 = 0 + 60.20408163 Combine like terms: 0 + 60.20408163 = 60.20408163 (38.57142857t) + t2 = 60.20408163 The t term is (38.57142857t). Take half its coefficient (19.28571429). Square it (371.9387757) and add it to both sides. Add '371.9387757' to each side of the equation. (38.57142857t) + 371.9387757 + t2 = 60.20408163 + 371.9387757 Reorder the terms: 371.9387757 + (38.57142857t) + t2 = 60.20408163 + 371.9387757 Combine like terms: 60.20408163 + 371.9387757 = 432.14285733 371.9387757 + (38.57142857t) + t2 = 432.14285733 Factor a perfect square on the left side: ((t) + 19.28571429)((t) + 19.28571429) = 432.14285733 Calculate the square root of the right side: 20.78804602 Break this problem into two subproblems by setting ((t) + 19.28571429) equal to 20.78804602 and -20.78804602.Subproblem 1
(t) + 19.28571429 = 20.78804602 Simplifying (t) + 19.28571429 = 20.78804602 t + 19.28571429 = 20.78804602 Reorder the terms: 19.28571429 + t = 20.78804602 Solving 19.28571429 + t = 20.78804602 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.28571429' to each side of the equation. 19.28571429 + -19.28571429 + t = 20.78804602 + -19.28571429 Combine like terms: 19.28571429 + -19.28571429 = 0.00000000 0.00000000 + t = 20.78804602 + -19.28571429 t = 20.78804602 + -19.28571429 Combine like terms: 20.78804602 + -19.28571429 = 1.50233173 t = 1.50233173 Simplifying t = 1.50233173Subproblem 2
(t) + 19.28571429 = -20.78804602 Simplifying (t) + 19.28571429 = -20.78804602 t + 19.28571429 = -20.78804602 Reorder the terms: 19.28571429 + t = -20.78804602 Solving 19.28571429 + t = -20.78804602 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.28571429' to each side of the equation. 19.28571429 + -19.28571429 + t = -20.78804602 + -19.28571429 Combine like terms: 19.28571429 + -19.28571429 = 0.00000000 0.00000000 + t = -20.78804602 + -19.28571429 t = -20.78804602 + -19.28571429 Combine like terms: -20.78804602 + -19.28571429 = -40.07376031 t = -40.07376031 Simplifying t = -40.07376031Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.50233173, -40.07376031}
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