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Simplifying x(x + -5) = 1 Reorder the terms: x(-5 + x) = 1 (-5 * x + x * x) = 1 (-5x + x2) = 1 Solving -5x + x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -5x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x + x2 = 0 + 1 -5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5x + x2 = 1 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 = 1 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + -5x + x2 = 7.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -2.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -2.5 = 2.692582404 Simplifying x + -2.5 = 2.692582404 Reorder the terms: -2.5 + x = 2.692582404 Solving -2.5 + x = 2.692582404 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 = 2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.692582404 + 2.5 x = 2.692582404 + 2.5 Combine like terms: 2.692582404 + 2.5 = 5.192582404 x = 5.192582404 Simplifying x = 5.192582404Subproblem 2
x + -2.5 = -2.692582404 Simplifying x + -2.5 = -2.692582404 Reorder the terms: -2.5 + x = -2.692582404 Solving -2.5 + x = -2.692582404 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 = -2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.692582404 + 2.5 x = -2.692582404 + 2.5 Combine like terms: -2.692582404 + 2.5 = -0.192582404 x = -0.192582404 Simplifying x = -0.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.192582404, -0.192582404}
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