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Simplifying 20 = -4t2 + 160t Reorder the terms: 20 = 160t + -4t2 Solving 20 = 160t + -4t2 Solving for variable 't'. Reorder the terms: 20 + -160t + 4t2 = 160t + -160t + -4t2 + 4t2 Combine like terms: 160t + -160t = 0 20 + -160t + 4t2 = 0 + -4t2 + 4t2 20 + -160t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 20 + -160t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -40t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -40t + t2)' equal to zero and attempt to solve: Simplifying 5 + -40t + t2 = 0 Solving 5 + -40t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -40t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -40t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -40t + t2 = 0 + -5 -40t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -40t + t2 = -5 The t term is -40t. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40t + 400 + t2 = -5 + 400 Reorder the terms: 400 + -40t + t2 = -5 + 400 Combine like terms: -5 + 400 = 395 400 + -40t + t2 = 395 Factor a perfect square on the left side: (t + -20)(t + -20) = 395 Calculate the square root of the right side: 19.874606914 Break this problem into two subproblems by setting (t + -20) equal to 19.874606914 and -19.874606914.Subproblem 1
t + -20 = 19.874606914 Simplifying t + -20 = 19.874606914 Reorder the terms: -20 + t = 19.874606914 Solving -20 + t = 19.874606914 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 19.874606914 + 20 Combine like terms: -20 + 20 = 0 0 + t = 19.874606914 + 20 t = 19.874606914 + 20 Combine like terms: 19.874606914 + 20 = 39.874606914 t = 39.874606914 Simplifying t = 39.874606914Subproblem 2
t + -20 = -19.874606914 Simplifying t + -20 = -19.874606914 Reorder the terms: -20 + t = -19.874606914 Solving -20 + t = -19.874606914 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -19.874606914 + 20 Combine like terms: -20 + 20 = 0 0 + t = -19.874606914 + 20 t = -19.874606914 + 20 Combine like terms: -19.874606914 + 20 = 0.125393086 t = 0.125393086 Simplifying t = 0.125393086Solution
The solution to the problem is based on the solutions from the subproblems. t = {39.874606914, 0.125393086}Solution
t = {39.874606914, 0.125393086}
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