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Simplifying 150 = 19t2 + -100t Reorder the terms: 150 = -100t + 19t2 Solving 150 = -100t + 19t2 Solving for variable 't'. Reorder the terms: 150 + 100t + -19t2 = -100t + 100t + 19t2 + -19t2 Combine like terms: -100t + 100t = 0 150 + 100t + -19t2 = 0 + 19t2 + -19t2 150 + 100t + -19t2 = 19t2 + -19t2 Combine like terms: 19t2 + -19t2 = 0 150 + 100t + -19t2 = 0 Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -7.894736842 + -5.263157895t + t2 = 0 Move the constant term to the right: Add '7.894736842' to each side of the equation. -7.894736842 + -5.263157895t + 7.894736842 + t2 = 0 + 7.894736842 Reorder the terms: -7.894736842 + 7.894736842 + -5.263157895t + t2 = 0 + 7.894736842 Combine like terms: -7.894736842 + 7.894736842 = 0.000000000 0.000000000 + -5.263157895t + t2 = 0 + 7.894736842 -5.263157895t + t2 = 0 + 7.894736842 Combine like terms: 0 + 7.894736842 = 7.894736842 -5.263157895t + t2 = 7.894736842 The t term is -5.263157895t. Take half its coefficient (-2.631578948). Square it (6.925207760) and add it to both sides. Add '6.925207760' to each side of the equation. -5.263157895t + 6.925207760 + t2 = 7.894736842 + 6.925207760 Reorder the terms: 6.925207760 + -5.263157895t + t2 = 7.894736842 + 6.925207760 Combine like terms: 7.894736842 + 6.925207760 = 14.819944602 6.925207760 + -5.263157895t + t2 = 14.819944602 Factor a perfect square on the left side: (t + -2.631578948)(t + -2.631578948) = 14.819944602 Calculate the square root of the right side: 3.849668116 Break this problem into two subproblems by setting (t + -2.631578948) equal to 3.849668116 and -3.849668116.Subproblem 1
t + -2.631578948 = 3.849668116 Simplifying t + -2.631578948 = 3.849668116 Reorder the terms: -2.631578948 + t = 3.849668116 Solving -2.631578948 + t = 3.849668116 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.631578948' to each side of the equation. -2.631578948 + 2.631578948 + t = 3.849668116 + 2.631578948 Combine like terms: -2.631578948 + 2.631578948 = 0.000000000 0.000000000 + t = 3.849668116 + 2.631578948 t = 3.849668116 + 2.631578948 Combine like terms: 3.849668116 + 2.631578948 = 6.481247064 t = 6.481247064 Simplifying t = 6.481247064Subproblem 2
t + -2.631578948 = -3.849668116 Simplifying t + -2.631578948 = -3.849668116 Reorder the terms: -2.631578948 + t = -3.849668116 Solving -2.631578948 + t = -3.849668116 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.631578948' to each side of the equation. -2.631578948 + 2.631578948 + t = -3.849668116 + 2.631578948 Combine like terms: -2.631578948 + 2.631578948 = 0.000000000 0.000000000 + t = -3.849668116 + 2.631578948 t = -3.849668116 + 2.631578948 Combine like terms: -3.849668116 + 2.631578948 = -1.218089168 t = -1.218089168 Simplifying t = -1.218089168Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.481247064, -1.218089168}
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