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Simplifying x(x + -6) = x * 2 + 3x + 5 Reorder the terms: x(-6 + x) = x * 2 + 3x + 5 (-6 * x + x * x) = x * 2 + 3x + 5 (-6x + x2) = x * 2 + 3x + 5 Reorder the terms for easier multiplication: -6x + x2 = 2x + 3x + 5 Reorder the terms: -6x + x2 = 5 + 2x + 3x Combine like terms: 2x + 3x = 5x -6x + x2 = 5 + 5x Solving -6x + x2 = 5 + 5x Solving for variable 'x'. Reorder the terms: -5 + -6x + -5x + x2 = 5 + 5x + -5 + -5x Combine like terms: -6x + -5x = -11x -5 + -11x + x2 = 5 + 5x + -5 + -5x Reorder the terms: -5 + -11x + x2 = 5 + -5 + 5x + -5x Combine like terms: 5 + -5 = 0 -5 + -11x + x2 = 0 + 5x + -5x -5 + -11x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -5 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -11x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -11x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -11x + x2 = 0 + 5 -11x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -11x + x2 = 5 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 5 + 30.25 Combine like terms: 5 + 30.25 = 35.25 30.25 + -11x + x2 = 35.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -5.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -5.5 = 5.937171044 Simplifying x + -5.5 = 5.937171044 Reorder the terms: -5.5 + x = 5.937171044 Solving -5.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.937171044 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.937171044 + 5.5 x = 5.937171044 + 5.5 Combine like terms: 5.937171044 + 5.5 = 11.437171044 x = 11.437171044 Simplifying x = 11.437171044Subproblem 2
x + -5.5 = -5.937171044 Simplifying x + -5.5 = -5.937171044 Reorder the terms: -5.5 + x = -5.937171044 Solving -5.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.937171044 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.937171044 + 5.5 x = -5.937171044 + 5.5 Combine like terms: -5.937171044 + 5.5 = -0.437171044 x = -0.437171044 Simplifying x = -0.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.437171044, -0.437171044}
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