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Simplifying 0.0825t2 + -1.872t + 1.864 = 0 Reorder the terms: 1.864 + -1.872t + 0.0825t2 = 0 Solving 1.864 + -1.872t + 0.0825t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0825 the coefficient of the squared term: Divide each side by '0.0825'. 22.59393939 + -22.69090909t + t2 = 0 Move the constant term to the right: Add '-22.59393939' to each side of the equation. 22.59393939 + -22.69090909t + -22.59393939 + t2 = 0 + -22.59393939 Reorder the terms: 22.59393939 + -22.59393939 + -22.69090909t + t2 = 0 + -22.59393939 Combine like terms: 22.59393939 + -22.59393939 = 0.00000000 0.00000000 + -22.69090909t + t2 = 0 + -22.59393939 -22.69090909t + t2 = 0 + -22.59393939 Combine like terms: 0 + -22.59393939 = -22.59393939 -22.69090909t + t2 = -22.59393939 The t term is -22.69090909t. Take half its coefficient (-11.34545455). Square it (128.7193389) and add it to both sides. Add '128.7193389' to each side of the equation. -22.69090909t + 128.7193389 + t2 = -22.59393939 + 128.7193389 Reorder the terms: 128.7193389 + -22.69090909t + t2 = -22.59393939 + 128.7193389 Combine like terms: -22.59393939 + 128.7193389 = 106.12539951 128.7193389 + -22.69090909t + t2 = 106.12539951 Factor a perfect square on the left side: (t + -11.34545455)(t + -11.34545455) = 106.12539951 Calculate the square root of the right side: 10.301718279 Break this problem into two subproblems by setting (t + -11.34545455) equal to 10.301718279 and -10.301718279.Subproblem 1
t + -11.34545455 = 10.301718279 Simplifying t + -11.34545455 = 10.301718279 Reorder the terms: -11.34545455 + t = 10.301718279 Solving -11.34545455 + t = 10.301718279 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.34545455' to each side of the equation. -11.34545455 + 11.34545455 + t = 10.301718279 + 11.34545455 Combine like terms: -11.34545455 + 11.34545455 = 0.00000000 0.00000000 + t = 10.301718279 + 11.34545455 t = 10.301718279 + 11.34545455 Combine like terms: 10.301718279 + 11.34545455 = 21.647172829 t = 21.647172829 Simplifying t = 21.647172829Subproblem 2
t + -11.34545455 = -10.301718279 Simplifying t + -11.34545455 = -10.301718279 Reorder the terms: -11.34545455 + t = -10.301718279 Solving -11.34545455 + t = -10.301718279 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.34545455' to each side of the equation. -11.34545455 + 11.34545455 + t = -10.301718279 + 11.34545455 Combine like terms: -11.34545455 + 11.34545455 = 0.00000000 0.00000000 + t = -10.301718279 + 11.34545455 t = -10.301718279 + 11.34545455 Combine like terms: -10.301718279 + 11.34545455 = 1.043736271 t = 1.043736271 Simplifying t = 1.043736271Solution
The solution to the problem is based on the solutions from the subproblems. t = {21.647172829, 1.043736271}
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