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Simplifying 0 = 20t + 5t2 + -125 Reorder the terms: 0 = -125 + 20t + 5t2 Solving 0 = -125 + 20t + 5t2 Solving for variable 't'. Combine like terms: 0 + 125 = 125 125 + -20t + -5t2 = -125 + 20t + 5t2 + 125 + -20t + -5t2 Reorder the terms: 125 + -20t + -5t2 = -125 + 125 + 20t + -20t + 5t2 + -5t2 Combine like terms: -125 + 125 = 0 125 + -20t + -5t2 = 0 + 20t + -20t + 5t2 + -5t2 125 + -20t + -5t2 = 20t + -20t + 5t2 + -5t2 Combine like terms: 20t + -20t = 0 125 + -20t + -5t2 = 0 + 5t2 + -5t2 125 + -20t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 125 + -20t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(25 + -4t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(25 + -4t + -1t2)' equal to zero and attempt to solve: Simplifying 25 + -4t + -1t2 = 0 Solving 25 + -4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 4t + t2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 4t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + 4t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4t + t2 = 0 + 25 4t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 4t + t2 = 25 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 25 + 4 Reorder the terms: 4 + 4t + t2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + 4t + t2 = 29 Factor a perfect square on the left side: (t + 2)(t + 2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (t + 2) equal to 5.385164807 and -5.385164807.Subproblem 1
t + 2 = 5.385164807 Simplifying t + 2 = 5.385164807 Reorder the terms: 2 + t = 5.385164807 Solving 2 + t = 5.385164807 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + t = 5.385164807 + -2 t = 5.385164807 + -2 Combine like terms: 5.385164807 + -2 = 3.385164807 t = 3.385164807 Simplifying t = 3.385164807Subproblem 2
t + 2 = -5.385164807 Simplifying t + 2 = -5.385164807 Reorder the terms: 2 + t = -5.385164807 Solving 2 + t = -5.385164807 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + t = -5.385164807 + -2 t = -5.385164807 + -2 Combine like terms: -5.385164807 + -2 = -7.385164807 t = -7.385164807 Simplifying t = -7.385164807Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.385164807, -7.385164807}Solution
t = {3.385164807, -7.385164807}
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