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Simplifying 500x + x2 = 1000 Solving 500x + x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + 500x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 500x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 500x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 500x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 500x + x2 = 0 + 1000 500x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 500x + x2 = 1000 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 = 1000 + 62500 Reorder the terms: 62500 + 500x + x2 = 1000 + 62500 Combine like terms: 1000 + 62500 = 63500 62500 + 500x + x2 = 63500 Factor a perfect square on the left side: (x + 250)(x + 250) = 63500 Calculate the square root of the right side: 251.992063367 Break this problem into two subproblems by setting (x + 250) equal to 251.992063367 and -251.992063367.Subproblem 1
x + 250 = 251.992063367 Simplifying x + 250 = 251.992063367 Reorder the terms: 250 + x = 251.992063367 Solving 250 + x = 251.992063367 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 = 251.992063367 + -250 Combine like terms: 250 + -250 = 0 0 + x = 251.992063367 + -250 x = 251.992063367 + -250 Combine like terms: 251.992063367 + -250 = 1.992063367 x = 1.992063367 Simplifying x = 1.992063367Subproblem 2
x + 250 = -251.992063367 Simplifying x + 250 = -251.992063367 Reorder the terms: 250 + x = -251.992063367 Solving 250 + x = -251.992063367 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 = -251.992063367 + -250 Combine like terms: 250 + -250 = 0 0 + x = -251.992063367 + -250 x = -251.992063367 + -250 Combine like terms: -251.992063367 + -250 = -501.992063367 x = -501.992063367 Simplifying x = -501.992063367Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.992063367, -501.992063367}
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