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Simplifying 550 = 16t2 + 208t Reorder the terms: 550 = 208t + 16t2 Solving 550 = 208t + 16t2 Solving for variable 't'. Reorder the terms: 550 + -208t + -16t2 = 208t + -208t + 16t2 + -16t2 Combine like terms: 208t + -208t = 0 550 + -208t + -16t2 = 0 + 16t2 + -16t2 550 + -208t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 550 + -208t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(275 + -104t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(275 + -104t + -8t2)' equal to zero and attempt to solve: Simplifying 275 + -104t + -8t2 = 0 Solving 275 + -104t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -34.375 + 13t + t2 = 0 Move the constant term to the right: Add '34.375' to each side of the equation. -34.375 + 13t + 34.375 + t2 = 0 + 34.375 Reorder the terms: -34.375 + 34.375 + 13t + t2 = 0 + 34.375 Combine like terms: -34.375 + 34.375 = 0.000 0.000 + 13t + t2 = 0 + 34.375 13t + t2 = 0 + 34.375 Combine like terms: 0 + 34.375 = 34.375 13t + t2 = 34.375 The t term is 13t. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13t + 42.25 + t2 = 34.375 + 42.25 Reorder the terms: 42.25 + 13t + t2 = 34.375 + 42.25 Combine like terms: 34.375 + 42.25 = 76.625 42.25 + 13t + t2 = 76.625 Factor a perfect square on the left side: (t + 6.5)(t + 6.5) = 76.625 Calculate the square root of the right side: 8.7535707 Break this problem into two subproblems by setting (t + 6.5) equal to 8.7535707 and -8.7535707.Subproblem 1
t + 6.5 = 8.7535707 Simplifying t + 6.5 = 8.7535707 Reorder the terms: 6.5 + t = 8.7535707 Solving 6.5 + t = 8.7535707 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + t = 8.7535707 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + t = 8.7535707 + -6.5 t = 8.7535707 + -6.5 Combine like terms: 8.7535707 + -6.5 = 2.2535707 t = 2.2535707 Simplifying t = 2.2535707Subproblem 2
t + 6.5 = -8.7535707 Simplifying t + 6.5 = -8.7535707 Reorder the terms: 6.5 + t = -8.7535707 Solving 6.5 + t = -8.7535707 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + t = -8.7535707 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + t = -8.7535707 + -6.5 t = -8.7535707 + -6.5 Combine like terms: -8.7535707 + -6.5 = -15.2535707 t = -15.2535707 Simplifying t = -15.2535707Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.2535707, -15.2535707}Solution
t = {2.2535707, -15.2535707}
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