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Simplifying 50 = -16t2 + 80t + 32 Reorder the terms: 50 = 32 + 80t + -16t2 Solving 50 = 32 + 80t + -16t2 Solving for variable 't'. Combine like terms: 50 + -32 = 18 18 + -80t + 16t2 = 32 + 80t + -16t2 + -32 + -80t + 16t2 Reorder the terms: 18 + -80t + 16t2 = 32 + -32 + 80t + -80t + -16t2 + 16t2 Combine like terms: 32 + -32 = 0 18 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2 18 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 18 + -80t + 16t2 = 0 + -16t2 + 16t2 18 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 18 + -80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -40t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -40t + 8t2)' equal to zero and attempt to solve: Simplifying 9 + -40t + 8t2 = 0 Solving 9 + -40t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -5t + t2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -5t + -1.125 + t2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -5t + t2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -5t + t2 = 0 + -1.125 -5t + t2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -5t + t2 = -1.125 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -1.125 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -1.125 + 6.25 Combine like terms: -1.125 + 6.25 = 5.125 6.25 + -5t + t2 = 5.125 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 5.125 Calculate the square root of the right side: 2.263846285 Break this problem into two subproblems by setting (t + -2.5) equal to 2.263846285 and -2.263846285.Subproblem 1
t + -2.5 = 2.263846285 Simplifying t + -2.5 = 2.263846285 Reorder the terms: -2.5 + t = 2.263846285 Solving -2.5 + t = 2.263846285 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.263846285 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.263846285 + 2.5 t = 2.263846285 + 2.5 Combine like terms: 2.263846285 + 2.5 = 4.763846285 t = 4.763846285 Simplifying t = 4.763846285Subproblem 2
t + -2.5 = -2.263846285 Simplifying t + -2.5 = -2.263846285 Reorder the terms: -2.5 + t = -2.263846285 Solving -2.5 + t = -2.263846285 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.263846285 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.263846285 + 2.5 t = -2.263846285 + 2.5 Combine like terms: -2.263846285 + 2.5 = 0.236153715 t = 0.236153715 Simplifying t = 0.236153715Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.763846285, 0.236153715}Solution
t = {4.763846285, 0.236153715}
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