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Simplifying 350 = -16t2 + 160t Reorder the terms: 350 = 160t + -16t2 Solving 350 = 160t + -16t2 Solving for variable 't'. Reorder the terms: 350 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 350 + -160t + 16t2 = 0 + -16t2 + 16t2 350 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 350 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(175 + -80t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(175 + -80t + 8t2)' equal to zero and attempt to solve: Simplifying 175 + -80t + 8t2 = 0 Solving 175 + -80t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 21.875 + -10t + t2 = 0 Move the constant term to the right: Add '-21.875' to each side of the equation. 21.875 + -10t + -21.875 + t2 = 0 + -21.875 Reorder the terms: 21.875 + -21.875 + -10t + t2 = 0 + -21.875 Combine like terms: 21.875 + -21.875 = 0.000 0.000 + -10t + t2 = 0 + -21.875 -10t + t2 = 0 + -21.875 Combine like terms: 0 + -21.875 = -21.875 -10t + t2 = -21.875 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -21.875 + 25 Reorder the terms: 25 + -10t + t2 = -21.875 + 25 Combine like terms: -21.875 + 25 = 3.125 25 + -10t + t2 = 3.125 Factor a perfect square on the left side: (t + -5)(t + -5) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (t + -5) equal to 1.767766953 and -1.767766953.Subproblem 1
t + -5 = 1.767766953 Simplifying t + -5 = 1.767766953 Reorder the terms: -5 + t = 1.767766953 Solving -5 + t = 1.767766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 1.767766953 + 5 Combine like terms: -5 + 5 = 0 0 + t = 1.767766953 + 5 t = 1.767766953 + 5 Combine like terms: 1.767766953 + 5 = 6.767766953 t = 6.767766953 Simplifying t = 6.767766953Subproblem 2
t + -5 = -1.767766953 Simplifying t + -5 = -1.767766953 Reorder the terms: -5 + t = -1.767766953 Solving -5 + t = -1.767766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -1.767766953 + 5 Combine like terms: -5 + 5 = 0 0 + t = -1.767766953 + 5 t = -1.767766953 + 5 Combine like terms: -1.767766953 + 5 = 3.232233047 t = 3.232233047 Simplifying t = 3.232233047Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.767766953, 3.232233047}Solution
t = {6.767766953, 3.232233047}
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