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Simplifying -1.9t2 + 26t = 26 Reorder the terms: 26t + -1.9t2 = 26 Solving 26t + -1.9t2 = 26 Solving for variable 't'. Reorder the terms: -26 + 26t + -1.9t2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 26t + -1.9t2 = 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 = 33.13019393 46.81440446 + -13.68421053t + t2 = 33.13019393 Factor a perfect square on the left side: (t + -6.842105265)(t + -6.842105265) = 33.13019393 Calculate the square root of the right side: 5.755883419 Break this problem into two subproblems by setting (t + -6.842105265) equal to 5.755883419 and -5.755883419.Subproblem 1
t + -6.842105265 = 5.755883419 Simplifying t + -6.842105265 = 5.755883419 Reorder the terms: -6.842105265 + t = 5.755883419 Solving -6.842105265 + t = 5.755883419 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 = 5.755883419 + 6.842105265 Combine like terms: -6.842105265 + 6.842105265 = 0.000000000 0.000000000 + t = 5.755883419 + 6.842105265 t = 5.755883419 + 6.842105265 Combine like terms: 5.755883419 + 6.842105265 = 12.597988684 t = 12.597988684 Simplifying t = 12.597988684Subproblem 2
t + -6.842105265 = -5.755883419 Simplifying t + -6.842105265 = -5.755883419 Reorder the terms: -6.842105265 + t = -5.755883419 Solving -6.842105265 + t = -5.755883419 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 = -5.755883419 + 6.842105265 Combine like terms: -6.842105265 + 6.842105265 = 0.000000000 0.000000000 + t = -5.755883419 + 6.842105265 t = -5.755883419 + 6.842105265 Combine like terms: -5.755883419 + 6.842105265 = 1.086221846 t = 1.086221846 Simplifying t = 1.086221846Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.597988684, 1.086221846}
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