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Simplifying x(x + -5) = 27 Reorder the terms: x(-5 + x) = 27 (-5 * x + x * x) = 27 (-5x + x2) = 27 Solving -5x + x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + -5x + x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -5x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -5x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -5x + x2 = 0 + 27 -5x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -5x + x2 = 27 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 = 27 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 27 + 6.25 Combine like terms: 27 + 6.25 = 33.25 6.25 + -5x + x2 = 33.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + -2.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + -2.5 = 5.766281297 Simplifying x + -2.5 = 5.766281297 Reorder the terms: -2.5 + x = 5.766281297 Solving -2.5 + x = 5.766281297 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 = 5.766281297 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.766281297 + 2.5 x = 5.766281297 + 2.5 Combine like terms: 5.766281297 + 2.5 = 8.266281297 x = 8.266281297 Simplifying x = 8.266281297Subproblem 2
x + -2.5 = -5.766281297 Simplifying x + -2.5 = -5.766281297 Reorder the terms: -2.5 + x = -5.766281297 Solving -2.5 + x = -5.766281297 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 = -5.766281297 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.766281297 + 2.5 x = -5.766281297 + 2.5 Combine like terms: -5.766281297 + 2.5 = -3.266281297 x = -3.266281297 Simplifying x = -3.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.266281297, -3.266281297}
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