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Simplifying 280 = 137t + -4.9t2 Solving 280 = 137t + -4.9t2 Solving for variable 't'. Reorder the terms: 280 + -137t + 4.9t2 = 137t + -137t + -4.9t2 + 4.9t2 Combine like terms: 137t + -137t = 0 280 + -137t + 4.9t2 = 0 + -4.9t2 + 4.9t2 280 + -137t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 280 + -137t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 57.14285714 + -27.95918367t + t2 = 0 Move the constant term to the right: Add '-57.14285714' to each side of the equation. 57.14285714 + -27.95918367t + -57.14285714 + t2 = 0 + -57.14285714 Reorder the terms: 57.14285714 + -57.14285714 + -27.95918367t + t2 = 0 + -57.14285714 Combine like terms: 57.14285714 + -57.14285714 = 0.00000000 0.00000000 + -27.95918367t + t2 = 0 + -57.14285714 -27.95918367t + t2 = 0 + -57.14285714 Combine like terms: 0 + -57.14285714 = -57.14285714 -27.95918367t + t2 = -57.14285714 The t term is -27.95918367t. Take half its coefficient (-13.97959184). Square it (195.4289880) and add it to both sides. Add '195.4289880' to each side of the equation. -27.95918367t + 195.4289880 + t2 = -57.14285714 + 195.4289880 Reorder the terms: 195.4289880 + -27.95918367t + t2 = -57.14285714 + 195.4289880 Combine like terms: -57.14285714 + 195.4289880 = 138.28613086 195.4289880 + -27.95918367t + t2 = 138.28613086 Factor a perfect square on the left side: (t + -13.97959184)(t + -13.97959184) = 138.28613086 Calculate the square root of the right side: 11.759512356 Break this problem into two subproblems by setting (t + -13.97959184) equal to 11.759512356 and -11.759512356.Subproblem 1
t + -13.97959184 = 11.759512356 Simplifying t + -13.97959184 = 11.759512356 Reorder the terms: -13.97959184 + t = 11.759512356 Solving -13.97959184 + t = 11.759512356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.97959184' to each side of the equation. -13.97959184 + 13.97959184 + t = 11.759512356 + 13.97959184 Combine like terms: -13.97959184 + 13.97959184 = 0.00000000 0.00000000 + t = 11.759512356 + 13.97959184 t = 11.759512356 + 13.97959184 Combine like terms: 11.759512356 + 13.97959184 = 25.739104196 t = 25.739104196 Simplifying t = 25.739104196Subproblem 2
t + -13.97959184 = -11.759512356 Simplifying t + -13.97959184 = -11.759512356 Reorder the terms: -13.97959184 + t = -11.759512356 Solving -13.97959184 + t = -11.759512356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.97959184' to each side of the equation. -13.97959184 + 13.97959184 + t = -11.759512356 + 13.97959184 Combine like terms: -13.97959184 + 13.97959184 = 0.00000000 0.00000000 + t = -11.759512356 + 13.97959184 t = -11.759512356 + 13.97959184 Combine like terms: -11.759512356 + 13.97959184 = 2.220079484 t = 2.220079484 Simplifying t = 2.220079484Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.739104196, 2.220079484}
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