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Simplifying 0 = 9t + -0.7t2 + 9 Reorder the terms: 0 = 9 + 9t + -0.7t2 Solving 0 = 9 + 9t + -0.7t2 Solving for variable 't'. Combine like terms: 0 + -9 = -9 -9 + -9t + 0.7t2 = 9 + 9t + -0.7t2 + -9 + -9t + 0.7t2 Reorder the terms: -9 + -9t + 0.7t2 = 9 + -9 + 9t + -9t + -0.7t2 + 0.7t2 Combine like terms: 9 + -9 = 0 -9 + -9t + 0.7t2 = 0 + 9t + -9t + -0.7t2 + 0.7t2 -9 + -9t + 0.7t2 = 9t + -9t + -0.7t2 + 0.7t2 Combine like terms: 9t + -9t = 0 -9 + -9t + 0.7t2 = 0 + -0.7t2 + 0.7t2 -9 + -9t + 0.7t2 = -0.7t2 + 0.7t2 Combine like terms: -0.7t2 + 0.7t2 = 0.0 -9 + -9t + 0.7t2 = 0.0 Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. -12.85714286 + -12.85714286t + t2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + -12.85714286t + 12.85714286 + t2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + -12.85714286t + t2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + -12.85714286t + t2 = 0 + 12.85714286 -12.85714286t + t2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 -12.85714286t + t2 = 12.85714286 The t term is -12.85714286t. Take half its coefficient (-6.42857143). Square it (41.32653063) and add it to both sides. Add '41.32653063' to each side of the equation. -12.85714286t + 41.32653063 + t2 = 12.85714286 + 41.32653063 Reorder the terms: 41.32653063 + -12.85714286t + t2 = 12.85714286 + 41.32653063 Combine like terms: 12.85714286 + 41.32653063 = 54.18367349 41.32653063 + -12.85714286t + t2 = 54.18367349 Factor a perfect square on the left side: (t + -6.42857143)(t + -6.42857143) = 54.18367349 Calculate the square root of the right side: 7.360956017 Break this problem into two subproblems by setting (t + -6.42857143) equal to 7.360956017 and -7.360956017.Subproblem 1
t + -6.42857143 = 7.360956017 Simplifying t + -6.42857143 = 7.360956017 Reorder the terms: -6.42857143 + t = 7.360956017 Solving -6.42857143 + t = 7.360956017 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + t = 7.360956017 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + t = 7.360956017 + 6.42857143 t = 7.360956017 + 6.42857143 Combine like terms: 7.360956017 + 6.42857143 = 13.789527447 t = 13.789527447 Simplifying t = 13.789527447Subproblem 2
t + -6.42857143 = -7.360956017 Simplifying t + -6.42857143 = -7.360956017 Reorder the terms: -6.42857143 + t = -7.360956017 Solving -6.42857143 + t = -7.360956017 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + t = -7.360956017 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + t = -7.360956017 + 6.42857143 t = -7.360956017 + 6.42857143 Combine like terms: -7.360956017 + 6.42857143 = -0.932384587 t = -0.932384587 Simplifying t = -0.932384587Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.789527447, -0.932384587}
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