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Simplifying x2 + -500x + 625 = 400 Reorder the terms: 625 + -500x + x2 = 400 Solving 625 + -500x + x2 = 400 Solving for variable 'x'. Reorder the terms: 625 + -400 + -500x + x2 = 400 + -400 Combine like terms: 625 + -400 = 225 225 + -500x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 225 + -500x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + -500x + -225 + x2 = 0 + -225 Reorder the terms: 225 + -225 + -500x + x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -500x + x2 = 0 + -225 -500x + x2 = 0 + -225 Combine like terms: 0 + -225 = -225 -500x + x2 = -225 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -225 + 62500 Reorder the terms: 62500 + -500x + x2 = -225 + 62500 Combine like terms: -225 + 62500 = 62275 62500 + -500x + x2 = 62275 Factor a perfect square on the left side: (x + -250)(x + -250) = 62275 Calculate the square root of the right side: 249.549594269 Break this problem into two subproblems by setting (x + -250) equal to 249.549594269 and -249.549594269.Subproblem 1
x + -250 = 249.549594269 Simplifying x + -250 = 249.549594269 Reorder the terms: -250 + x = 249.549594269 Solving -250 + x = 249.549594269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 249.549594269 + 250 Combine like terms: -250 + 250 = 0 0 + x = 249.549594269 + 250 x = 249.549594269 + 250 Combine like terms: 249.549594269 + 250 = 499.549594269 x = 499.549594269 Simplifying x = 499.549594269Subproblem 2
x + -250 = -249.549594269 Simplifying x + -250 = -249.549594269 Reorder the terms: -250 + x = -249.549594269 Solving -250 + x = -249.549594269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -249.549594269 + 250 Combine like terms: -250 + 250 = 0 0 + x = -249.549594269 + 250 x = -249.549594269 + 250 Combine like terms: -249.549594269 + 250 = 0.450405731 x = 0.450405731 Simplifying x = 0.450405731Solution
The solution to the problem is based on the solutions from the subproblems. x = {499.549594269, 0.450405731}
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