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Simplifying x2 + -5x = 1000 Reorder the terms: -5x + x2 = 1000 Solving -5x + x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + -5x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -5x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -5x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -5x + x2 = 0 + 1000 -5x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -5x + x2 = 1000 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1000 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1000 + 6.25 Combine like terms: 1000 + 6.25 = 1006.25 6.25 + -5x + x2 = 1006.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1006.25 Calculate the square root of the right side: 31.721443851 Break this problem into two subproblems by setting (x + -2.5) equal to 31.721443851 and -31.721443851.Subproblem 1
x + -2.5 = 31.721443851 Simplifying x + -2.5 = 31.721443851 Reorder the terms: -2.5 + x = 31.721443851 Solving -2.5 + x = 31.721443851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 31.721443851 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 31.721443851 + 2.5 x = 31.721443851 + 2.5 Combine like terms: 31.721443851 + 2.5 = 34.221443851 x = 34.221443851 Simplifying x = 34.221443851Subproblem 2
x + -2.5 = -31.721443851 Simplifying x + -2.5 = -31.721443851 Reorder the terms: -2.5 + x = -31.721443851 Solving -2.5 + x = -31.721443851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -31.721443851 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -31.721443851 + 2.5 x = -31.721443851 + 2.5 Combine like terms: -31.721443851 + 2.5 = -29.221443851 x = -29.221443851 Simplifying x = -29.221443851Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.221443851, -29.221443851}
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