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Simplifying 26 = 1.9t2 + 26t Reorder the terms: 26 = 26t + 1.9t2 Solving 26 = 26t + 1.9t2 Solving for variable 't'. Reorder the terms: 26 + -26t + -1.9t2 = 26t + -26t + 1.9t2 + -1.9t2 Combine like terms: 26t + -26t = 0 26 + -26t + -1.9t2 = 0 + 1.9t2 + -1.9t2 26 + -26t + -1.9t2 = 1.9t2 + -1.9t2 Combine like terms: 1.9t2 + -1.9t2 = 0.0 26 + -26t + -1.9t2 = 0.0 Begin completing the square. Divide all terms by -1.9 the coefficient of the squared term: Divide each side by '-1.9'. -13.68421053 + 13.68421053t + t2 = 0 Move the constant term to the right: Add '13.68421053' to each side of the equation. -13.68421053 + 13.68421053t + 13.68421053 + t2 = 0 + 13.68421053 Reorder the terms: -13.68421053 + 13.68421053 + 13.68421053t + t2 = 0 + 13.68421053 Combine like terms: -13.68421053 + 13.68421053 = 0.00000000 0.00000000 + 13.68421053t + t2 = 0 + 13.68421053 13.68421053t + t2 = 0 + 13.68421053 Combine like terms: 0 + 13.68421053 = 13.68421053 13.68421053t + t2 = 13.68421053 The t term is 13.68421053t. Take half its coefficient (6.842105265). Square it (46.81440446) and add it to both sides. Add '46.81440446' to each side of the equation. 13.68421053t + 46.81440446 + t2 = 13.68421053 + 46.81440446 Reorder the terms: 46.81440446 + 13.68421053t + t2 = 13.68421053 + 46.81440446 Combine like terms: 13.68421053 + 46.81440446 = 60.49861499 46.81440446 + 13.68421053t + t2 = 60.49861499 Factor a perfect square on the left side: (t + 6.842105265)(t + 6.842105265) = 60.49861499 Calculate the square root of the right side: 7.778085561 Break this problem into two subproblems by setting (t + 6.842105265) equal to 7.778085561 and -7.778085561.Subproblem 1
t + 6.842105265 = 7.778085561 Simplifying t + 6.842105265 = 7.778085561 Reorder the terms: 6.842105265 + t = 7.778085561 Solving 6.842105265 + t = 7.778085561 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.842105265' to each side of the equation. 6.842105265 + -6.842105265 + t = 7.778085561 + -6.842105265 Combine like terms: 6.842105265 + -6.842105265 = 0.000000000 0.000000000 + t = 7.778085561 + -6.842105265 t = 7.778085561 + -6.842105265 Combine like terms: 7.778085561 + -6.842105265 = 0.935980296 t = 0.935980296 Simplifying t = 0.935980296Subproblem 2
t + 6.842105265 = -7.778085561 Simplifying t + 6.842105265 = -7.778085561 Reorder the terms: 6.842105265 + t = -7.778085561 Solving 6.842105265 + t = -7.778085561 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.842105265' to each side of the equation. 6.842105265 + -6.842105265 + t = -7.778085561 + -6.842105265 Combine like terms: 6.842105265 + -6.842105265 = 0.000000000 0.000000000 + t = -7.778085561 + -6.842105265 t = -7.778085561 + -6.842105265 Combine like terms: -7.778085561 + -6.842105265 = -14.620190826 t = -14.620190826 Simplifying t = -14.620190826Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.935980296, -14.620190826}
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