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Simplifying 50 = 126t + -16t2 Solving 50 = 126t + -16t2 Solving for variable 't'. Reorder the terms: 50 + -126t + 16t2 = 126t + -126t + -16t2 + 16t2 Combine like terms: 126t + -126t = 0 50 + -126t + 16t2 = 0 + -16t2 + 16t2 50 + -126t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 50 + -126t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -63t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -63t + 8t2)' equal to zero and attempt to solve: Simplifying 25 + -63t + 8t2 = 0 Solving 25 + -63t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.125 + -7.875t + t2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -7.875t + -3.125 + t2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -7.875t + t2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -7.875t + t2 = 0 + -3.125 -7.875t + t2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -7.875t + t2 = -3.125 The t term is -7.875t. Take half its coefficient (-3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. -7.875t + 15.50390625 + t2 = -3.125 + 15.50390625 Reorder the terms: 15.50390625 + -7.875t + t2 = -3.125 + 15.50390625 Combine like terms: -3.125 + 15.50390625 = 12.37890625 15.50390625 + -7.875t + t2 = 12.37890625 Factor a perfect square on the left side: (t + -3.9375)(t + -3.9375) = 12.37890625 Calculate the square root of the right side: 3.518366986 Break this problem into two subproblems by setting (t + -3.9375) equal to 3.518366986 and -3.518366986.Subproblem 1
t + -3.9375 = 3.518366986 Simplifying t + -3.9375 = 3.518366986 Reorder the terms: -3.9375 + t = 3.518366986 Solving -3.9375 + t = 3.518366986 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + t = 3.518366986 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + t = 3.518366986 + 3.9375 t = 3.518366986 + 3.9375 Combine like terms: 3.518366986 + 3.9375 = 7.455866986 t = 7.455866986 Simplifying t = 7.455866986Subproblem 2
t + -3.9375 = -3.518366986 Simplifying t + -3.9375 = -3.518366986 Reorder the terms: -3.9375 + t = -3.518366986 Solving -3.9375 + t = -3.518366986 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + t = -3.518366986 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + t = -3.518366986 + 3.9375 t = -3.518366986 + 3.9375 Combine like terms: -3.518366986 + 3.9375 = 0.419133014 t = 0.419133014 Simplifying t = 0.419133014Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.455866986, 0.419133014}Solution
t = {7.455866986, 0.419133014}
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