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Simplifying 5t2 + 20t = 625 Reorder the terms: 20t + 5t2 = 625 Solving 20t + 5t2 = 625 Solving for variable 't'. Reorder the terms: -625 + 20t + 5t2 = 625 + -625 Combine like terms: 625 + -625 = 0 -625 + 20t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-125 + 4t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-125 + 4t + t2)' equal to zero and attempt to solve: Simplifying -125 + 4t + t2 = 0 Solving -125 + 4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 4t + 125 + t2 = 0 + 125 Reorder the terms: -125 + 125 + 4t + t2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 4t + t2 = 0 + 125 4t + t2 = 0 + 125 Combine like terms: 0 + 125 = 125 4t + t2 = 125 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 = 125 + 4 Reorder the terms: 4 + 4t + t2 = 125 + 4 Combine like terms: 125 + 4 = 129 4 + 4t + t2 = 129 Factor a perfect square on the left side: (t + 2)(t + 2) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (t + 2) equal to 11.357816692 and -11.357816692.Subproblem 1
t + 2 = 11.357816692 Simplifying t + 2 = 11.357816692 Reorder the terms: 2 + t = 11.357816692 Solving 2 + t = 11.357816692 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 = 11.357816692 + -2 Combine like terms: 2 + -2 = 0 0 + t = 11.357816692 + -2 t = 11.357816692 + -2 Combine like terms: 11.357816692 + -2 = 9.357816692 t = 9.357816692 Simplifying t = 9.357816692Subproblem 2
t + 2 = -11.357816692 Simplifying t + 2 = -11.357816692 Reorder the terms: 2 + t = -11.357816692 Solving 2 + t = -11.357816692 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 = -11.357816692 + -2 Combine like terms: 2 + -2 = 0 0 + t = -11.357816692 + -2 t = -11.357816692 + -2 Combine like terms: -11.357816692 + -2 = -13.357816692 t = -13.357816692 Simplifying t = -13.357816692Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.357816692, -13.357816692}Solution
t = {9.357816692, -13.357816692}
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