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Simplifying x2 + -500x + 52000 = 0 Reorder the terms: 52000 + -500x + x2 = 0 Solving 52000 + -500x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-52000' to each side of the equation. 52000 + -500x + -52000 + x2 = 0 + -52000 Reorder the terms: 52000 + -52000 + -500x + x2 = 0 + -52000 Combine like terms: 52000 + -52000 = 0 0 + -500x + x2 = 0 + -52000 -500x + x2 = 0 + -52000 Combine like terms: 0 + -52000 = -52000 -500x + x2 = -52000 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 = -52000 + 62500 Reorder the terms: 62500 + -500x + x2 = -52000 + 62500 Combine like terms: -52000 + 62500 = 10500 62500 + -500x + x2 = 10500 Factor a perfect square on the left side: (x + -250)(x + -250) = 10500 Calculate the square root of the right side: 102.46950766 Break this problem into two subproblems by setting (x + -250) equal to 102.46950766 and -102.46950766.Subproblem 1
x + -250 = 102.46950766 Simplifying x + -250 = 102.46950766 Reorder the terms: -250 + x = 102.46950766 Solving -250 + x = 102.46950766 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 = 102.46950766 + 250 Combine like terms: -250 + 250 = 0 0 + x = 102.46950766 + 250 x = 102.46950766 + 250 Combine like terms: 102.46950766 + 250 = 352.46950766 x = 352.46950766 Simplifying x = 352.46950766Subproblem 2
x + -250 = -102.46950766 Simplifying x + -250 = -102.46950766 Reorder the terms: -250 + x = -102.46950766 Solving -250 + x = -102.46950766 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 = -102.46950766 + 250 Combine like terms: -250 + 250 = 0 0 + x = -102.46950766 + 250 x = -102.46950766 + 250 Combine like terms: -102.46950766 + 250 = 147.53049234 x = 147.53049234 Simplifying x = 147.53049234Solution
The solution to the problem is based on the solutions from the subproblems. x = {352.46950766, 147.53049234}
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