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Simplifying 400(t) = 400 + -16t2 Solving 400t = 400 + -16t2 Solving for variable 't'. Reorder the terms: -400 + 400t + 16t2 = 400 + -16t2 + -400 + 16t2 Reorder the terms: -400 + 400t + 16t2 = 400 + -400 + -16t2 + 16t2 Combine like terms: 400 + -400 = 0 -400 + 400t + 16t2 = 0 + -16t2 + 16t2 -400 + 400t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -400 + 400t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-25 + 25t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-25 + 25t + t2)' equal to zero and attempt to solve: Simplifying -25 + 25t + t2 = 0 Solving -25 + 25t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 25t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + 25t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 25t + t2 = 0 + 25 25t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 25t + t2 = 25 The t term is 25t. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25t + 156.25 + t2 = 25 + 156.25 Reorder the terms: 156.25 + 25t + t2 = 25 + 156.25 Combine like terms: 25 + 156.25 = 181.25 156.25 + 25t + t2 = 181.25 Factor a perfect square on the left side: (t + 12.5)(t + 12.5) = 181.25 Calculate the square root of the right side: 13.462912018 Break this problem into two subproblems by setting (t + 12.5) equal to 13.462912018 and -13.462912018.Subproblem 1
t + 12.5 = 13.462912018 Simplifying t + 12.5 = 13.462912018 Reorder the terms: 12.5 + t = 13.462912018 Solving 12.5 + t = 13.462912018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + t = 13.462912018 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + t = 13.462912018 + -12.5 t = 13.462912018 + -12.5 Combine like terms: 13.462912018 + -12.5 = 0.962912018 t = 0.962912018 Simplifying t = 0.962912018Subproblem 2
t + 12.5 = -13.462912018 Simplifying t + 12.5 = -13.462912018 Reorder the terms: 12.5 + t = -13.462912018 Solving 12.5 + t = -13.462912018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + t = -13.462912018 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + t = -13.462912018 + -12.5 t = -13.462912018 + -12.5 Combine like terms: -13.462912018 + -12.5 = -25.962912018 t = -25.962912018 Simplifying t = -25.962912018Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.962912018, -25.962912018}Solution
t = {0.962912018, -25.962912018}
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