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Simplifying (16t2) + -800t + -6400 = 0 Reorder the terms: -6400 + -800t + (16t2) = 0 Solving -6400 + -800t + (16t2) = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(-400 + -50t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-400 + -50t + t2)' equal to zero and attempt to solve: Simplifying -400 + -50t + t2 = 0 Solving -400 + -50t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -50t + 400 + t2 = 0 + 400 Reorder the terms: -400 + 400 + -50t + t2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -50t + t2 = 0 + 400 -50t + t2 = 0 + 400 Combine like terms: 0 + 400 = 400 -50t + t2 = 400 The t term is -50t. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50t + 625 + t2 = 400 + 625 Reorder the terms: 625 + -50t + t2 = 400 + 625 Combine like terms: 400 + 625 = 1025 625 + -50t + t2 = 1025 Factor a perfect square on the left side: (t + -25)(t + -25) = 1025 Calculate the square root of the right side: 32.015621187 Break this problem into two subproblems by setting (t + -25) equal to 32.015621187 and -32.015621187.Subproblem 1
t + -25 = 32.015621187 Simplifying t + -25 = 32.015621187 Reorder the terms: -25 + t = 32.015621187 Solving -25 + t = 32.015621187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = 32.015621187 + 25 Combine like terms: -25 + 25 = 0 0 + t = 32.015621187 + 25 t = 32.015621187 + 25 Combine like terms: 32.015621187 + 25 = 57.015621187 t = 57.015621187 Simplifying t = 57.015621187Subproblem 2
t + -25 = -32.015621187 Simplifying t + -25 = -32.015621187 Reorder the terms: -25 + t = -32.015621187 Solving -25 + t = -32.015621187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = -32.015621187 + 25 Combine like terms: -25 + 25 = 0 0 + t = -32.015621187 + 25 t = -32.015621187 + 25 Combine like terms: -32.015621187 + 25 = -7.015621187 t = -7.015621187 Simplifying t = -7.015621187Solution
The solution to the problem is based on the solutions from the subproblems. t = {57.015621187, -7.015621187}Solution
t = {57.015621187, -7.015621187}
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