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Simplifying 8 = 2 + 14t + -4.9t2 Solving 8 = 2 + 14t + -4.9t2 Solving for variable 't'. Combine like terms: 8 + -2 = 6 6 + -14t + 4.9t2 = 2 + 14t + -4.9t2 + -2 + -14t + 4.9t2 Reorder the terms: 6 + -14t + 4.9t2 = 2 + -2 + 14t + -14t + -4.9t2 + 4.9t2 Combine like terms: 2 + -2 = 0 6 + -14t + 4.9t2 = 0 + 14t + -14t + -4.9t2 + 4.9t2 6 + -14t + 4.9t2 = 14t + -14t + -4.9t2 + 4.9t2 Combine like terms: 14t + -14t = 0 6 + -14t + 4.9t2 = 0 + -4.9t2 + 4.9t2 6 + -14t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 6 + -14t + 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'. 1.224489796 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '-1.224489796' to each side of the equation. 1.224489796 + -2.857142857t + -1.224489796 + t2 = 0 + -1.224489796 Reorder the terms: 1.224489796 + -1.224489796 + -2.857142857t + t2 = 0 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + -2.857142857t + t2 = 0 + -1.224489796 -2.857142857t + t2 = 0 + -1.224489796 Combine like terms: 0 + -1.224489796 = -1.224489796 -2.857142857t + t2 = -1.224489796 The t term is -2.857142857t. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857t + 2.040816328 + t2 = -1.224489796 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = -1.224489796 + 2.040816328 Combine like terms: -1.224489796 + 2.040816328 = 0.816326532 2.040816328 + -2.857142857t + t2 = 0.816326532 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 0.816326532 Calculate the square root of the right side: 0.903507904 Break this problem into two subproblems by setting (t + -1.428571429) equal to 0.903507904 and -0.903507904.Subproblem 1
t + -1.428571429 = 0.903507904 Simplifying t + -1.428571429 = 0.903507904 Reorder the terms: -1.428571429 + t = 0.903507904 Solving -1.428571429 + t = 0.903507904 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 0.903507904 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 0.903507904 + 1.428571429 t = 0.903507904 + 1.428571429 Combine like terms: 0.903507904 + 1.428571429 = 2.332079333 t = 2.332079333 Simplifying t = 2.332079333Subproblem 2
t + -1.428571429 = -0.903507904 Simplifying t + -1.428571429 = -0.903507904 Reorder the terms: -1.428571429 + t = -0.903507904 Solving -1.428571429 + t = -0.903507904 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -0.903507904 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -0.903507904 + 1.428571429 t = -0.903507904 + 1.428571429 Combine like terms: -0.903507904 + 1.428571429 = 0.525063525 t = 0.525063525 Simplifying t = 0.525063525Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.332079333, 0.525063525}
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