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Simplifying 9t + -1(0.7) * t2 + 7 = 0 Multiply -1 * 0.7 9t + -0.7t2 + 7 = 0 Reorder the terms: 7 + 9t + -0.7t2 = 0 Solving 7 + 9t + -0.7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -10 + -12.85714286t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -12.85714286t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -12.85714286t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -12.85714286t + t2 = 0 + 10 -12.85714286t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -12.85714286t + t2 = 10 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 = 10 + 41.32653063 Reorder the terms: 41.32653063 + -12.85714286t + t2 = 10 + 41.32653063 Combine like terms: 10 + 41.32653063 = 51.32653063 41.32653063 + -12.85714286t + t2 = 51.32653063 Factor a perfect square on the left side: (t + -6.42857143)(t + -6.42857143) = 51.32653063 Calculate the square root of the right side: 7.164253669 Break this problem into two subproblems by setting (t + -6.42857143) equal to 7.164253669 and -7.164253669.Subproblem 1
t + -6.42857143 = 7.164253669 Simplifying t + -6.42857143 = 7.164253669 Reorder the terms: -6.42857143 + t = 7.164253669 Solving -6.42857143 + t = 7.164253669 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 = 7.164253669 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + t = 7.164253669 + 6.42857143 t = 7.164253669 + 6.42857143 Combine like terms: 7.164253669 + 6.42857143 = 13.592825099 t = 13.592825099 Simplifying t = 13.592825099Subproblem 2
t + -6.42857143 = -7.164253669 Simplifying t + -6.42857143 = -7.164253669 Reorder the terms: -6.42857143 + t = -7.164253669 Solving -6.42857143 + t = -7.164253669 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 = -7.164253669 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + t = -7.164253669 + 6.42857143 t = -7.164253669 + 6.42857143 Combine like terms: -7.164253669 + 6.42857143 = -0.735682239 t = -0.735682239 Simplifying t = -0.735682239Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.592825099, -0.735682239}
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