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Simplifying 4t2 + -20t + 20 = 0 Reorder the terms: 20 + -20t + 4t2 = 0 Solving 20 + -20t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -5t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -5t + t2)' equal to zero and attempt to solve: Simplifying 5 + -5t + t2 = 0 Solving 5 + -5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -5t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5t + t2 = 0 + -5 -5t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5t + t2 = -5 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 = -5 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + -5t + t2 = 1.25 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (t + -2.5) equal to 1.118033989 and -1.118033989.Subproblem 1
t + -2.5 = 1.118033989 Simplifying t + -2.5 = 1.118033989 Reorder the terms: -2.5 + t = 1.118033989 Solving -2.5 + t = 1.118033989 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 = 1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 1.118033989 + 2.5 t = 1.118033989 + 2.5 Combine like terms: 1.118033989 + 2.5 = 3.618033989 t = 3.618033989 Simplifying t = 3.618033989Subproblem 2
t + -2.5 = -1.118033989 Simplifying t + -2.5 = -1.118033989 Reorder the terms: -2.5 + t = -1.118033989 Solving -2.5 + t = -1.118033989 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 = -1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -1.118033989 + 2.5 t = -1.118033989 + 2.5 Combine like terms: -1.118033989 + 2.5 = 1.381966011 t = 1.381966011 Simplifying t = 1.381966011Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.618033989, 1.381966011}Solution
t = {3.618033989, 1.381966011}
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