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Simplifying 50 = 3 + 48t + -8t2 Solving 50 = 3 + 48t + -8t2 Solving for variable 't'. Combine like terms: 50 + -3 = 47 47 + -48t + 8t2 = 3 + 48t + -8t2 + -3 + -48t + 8t2 Reorder the terms: 47 + -48t + 8t2 = 3 + -3 + 48t + -48t + -8t2 + 8t2 Combine like terms: 3 + -3 = 0 47 + -48t + 8t2 = 0 + 48t + -48t + -8t2 + 8t2 47 + -48t + 8t2 = 48t + -48t + -8t2 + 8t2 Combine like terms: 48t + -48t = 0 47 + -48t + 8t2 = 0 + -8t2 + 8t2 47 + -48t + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 47 + -48t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.875 + -6t + t2 = 0 Move the constant term to the right: Add '-5.875' to each side of the equation. 5.875 + -6t + -5.875 + t2 = 0 + -5.875 Reorder the terms: 5.875 + -5.875 + -6t + t2 = 0 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + -6t + t2 = 0 + -5.875 -6t + t2 = 0 + -5.875 Combine like terms: 0 + -5.875 = -5.875 -6t + t2 = -5.875 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -5.875 + 9 Reorder the terms: 9 + -6t + t2 = -5.875 + 9 Combine like terms: -5.875 + 9 = 3.125 9 + -6t + t2 = 3.125 Factor a perfect square on the left side: (t + -3)(t + -3) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (t + -3) equal to 1.767766953 and -1.767766953.Subproblem 1
t + -3 = 1.767766953 Simplifying t + -3 = 1.767766953 Reorder the terms: -3 + t = 1.767766953 Solving -3 + t = 1.767766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 1.767766953 + 3 Combine like terms: -3 + 3 = 0 0 + t = 1.767766953 + 3 t = 1.767766953 + 3 Combine like terms: 1.767766953 + 3 = 4.767766953 t = 4.767766953 Simplifying t = 4.767766953Subproblem 2
t + -3 = -1.767766953 Simplifying t + -3 = -1.767766953 Reorder the terms: -3 + t = -1.767766953 Solving -3 + t = -1.767766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -1.767766953 + 3 Combine like terms: -3 + 3 = 0 0 + t = -1.767766953 + 3 t = -1.767766953 + 3 Combine like terms: -1.767766953 + 3 = 1.232233047 t = 1.232233047 Simplifying t = 1.232233047Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.767766953, 1.232233047}
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