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Simplifying 88 = 14t + 0.5(-0.41t2) Remove parenthesis around (-0.41t2) 88 = 14t + 0.5 * -0.41t2 Multiply 0.5 * -0.41 88 = 14t + -0.205t2 Solving 88 = 14t + -0.205t2 Solving for variable 't'. Reorder the terms: 88 + -14t + 0.205t2 = 14t + -14t + -0.205t2 + 0.205t2 Combine like terms: 14t + -14t = 0 88 + -14t + 0.205t2 = 0 + -0.205t2 + 0.205t2 88 + -14t + 0.205t2 = -0.205t2 + 0.205t2 Combine like terms: -0.205t2 + 0.205t2 = 0.000 88 + -14t + 0.205t2 = 0.000 Begin completing the square. Divide all terms by 0.205 the coefficient of the squared term: Divide each side by '0.205'. 429.2682927 + -68.29268293t + t2 = 0 Move the constant term to the right: Add '-429.2682927' to each side of the equation. 429.2682927 + -68.29268293t + -429.2682927 + t2 = 0 + -429.2682927 Reorder the terms: 429.2682927 + -429.2682927 + -68.29268293t + t2 = 0 + -429.2682927 Combine like terms: 429.2682927 + -429.2682927 = 0.0000000 0.0000000 + -68.29268293t + t2 = 0 + -429.2682927 -68.29268293t + t2 = 0 + -429.2682927 Combine like terms: 0 + -429.2682927 = -429.2682927 -68.29268293t + t2 = -429.2682927 The t term is -68.29268293t. Take half its coefficient (-34.14634147). Square it (1165.972636) and add it to both sides. Add '1165.972636' to each side of the equation. -68.29268293t + 1165.972636 + t2 = -429.2682927 + 1165.972636 Reorder the terms: 1165.972636 + -68.29268293t + t2 = -429.2682927 + 1165.972636 Combine like terms: -429.2682927 + 1165.972636 = 736.7043433 1165.972636 + -68.29268293t + t2 = 736.7043433 Factor a perfect square on the left side: (t + -34.14634147)(t + -34.14634147) = 736.7043433 Calculate the square root of the right side: 27.142298048 Break this problem into two subproblems by setting (t + -34.14634147) equal to 27.142298048 and -27.142298048.Subproblem 1
t + -34.14634147 = 27.142298048 Simplifying t + -34.14634147 = 27.142298048 Reorder the terms: -34.14634147 + t = 27.142298048 Solving -34.14634147 + t = 27.142298048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '34.14634147' to each side of the equation. -34.14634147 + 34.14634147 + t = 27.142298048 + 34.14634147 Combine like terms: -34.14634147 + 34.14634147 = 0.00000000 0.00000000 + t = 27.142298048 + 34.14634147 t = 27.142298048 + 34.14634147 Combine like terms: 27.142298048 + 34.14634147 = 61.288639518 t = 61.288639518 Simplifying t = 61.288639518Subproblem 2
t + -34.14634147 = -27.142298048 Simplifying t + -34.14634147 = -27.142298048 Reorder the terms: -34.14634147 + t = -27.142298048 Solving -34.14634147 + t = -27.142298048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '34.14634147' to each side of the equation. -34.14634147 + 34.14634147 + t = -27.142298048 + 34.14634147 Combine like terms: -34.14634147 + 34.14634147 = 0.00000000 0.00000000 + t = -27.142298048 + 34.14634147 t = -27.142298048 + 34.14634147 Combine like terms: -27.142298048 + 34.14634147 = 7.004043422 t = 7.004043422 Simplifying t = 7.004043422Solution
The solution to the problem is based on the solutions from the subproblems. t = {61.288639518, 7.004043422}
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