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Simplifying 1125 = 2500t + -5t2 Solving 1125 = 2500t + -5t2 Solving for variable 't'. Reorder the terms: 1125 + -2500t + 5t2 = 2500t + -2500t + -5t2 + 5t2 Combine like terms: 2500t + -2500t = 0 1125 + -2500t + 5t2 = 0 + -5t2 + 5t2 1125 + -2500t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 1125 + -2500t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(225 + -500t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(225 + -500t + t2)' equal to zero and attempt to solve: Simplifying 225 + -500t + t2 = 0 Solving 225 + -500t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + -500t + -225 + t2 = 0 + -225 Reorder the terms: 225 + -225 + -500t + t2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -500t + t2 = 0 + -225 -500t + t2 = 0 + -225 Combine like terms: 0 + -225 = -225 -500t + t2 = -225 The t term is -500t. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500t + 62500 + t2 = -225 + 62500 Reorder the terms: 62500 + -500t + t2 = -225 + 62500 Combine like terms: -225 + 62500 = 62275 62500 + -500t + t2 = 62275 Factor a perfect square on the left side: (t + -250)(t + -250) = 62275 Calculate the square root of the right side: 249.549594269 Break this problem into two subproblems by setting (t + -250) equal to 249.549594269 and -249.549594269.Subproblem 1
t + -250 = 249.549594269 Simplifying t + -250 = 249.549594269 Reorder the terms: -250 + t = 249.549594269 Solving -250 + t = 249.549594269 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + t = 249.549594269 + 250 Combine like terms: -250 + 250 = 0 0 + t = 249.549594269 + 250 t = 249.549594269 + 250 Combine like terms: 249.549594269 + 250 = 499.549594269 t = 499.549594269 Simplifying t = 499.549594269Subproblem 2
t + -250 = -249.549594269 Simplifying t + -250 = -249.549594269 Reorder the terms: -250 + t = -249.549594269 Solving -250 + t = -249.549594269 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + t = -249.549594269 + 250 Combine like terms: -250 + 250 = 0 0 + t = -249.549594269 + 250 t = -249.549594269 + 250 Combine like terms: -249.549594269 + 250 = 0.450405731 t = 0.450405731 Simplifying t = 0.450405731Solution
The solution to the problem is based on the solutions from the subproblems. t = {499.549594269, 0.450405731}Solution
t = {499.549594269, 0.450405731}
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