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Simplifying (x + -1)(x + -5) = 5x + 25 Reorder the terms: (-1 + x)(x + -5) = 5x + 25 Reorder the terms: (-1 + x)(-5 + x) = 5x + 25 Multiply (-1 + x) * (-5 + x) (-1(-5 + x) + x(-5 + x)) = 5x + 25 ((-5 * -1 + x * -1) + x(-5 + x)) = 5x + 25 ((5 + -1x) + x(-5 + x)) = 5x + 25 (5 + -1x + (-5 * x + x * x)) = 5x + 25 (5 + -1x + (-5x + x2)) = 5x + 25 Combine like terms: -1x + -5x = -6x (5 + -6x + x2) = 5x + 25 Reorder the terms: 5 + -6x + x2 = 25 + 5x Solving 5 + -6x + x2 = 25 + 5x Solving for variable 'x'. Reorder the terms: 5 + -25 + -6x + -5x + x2 = 25 + 5x + -25 + -5x Combine like terms: 5 + -25 = -20 -20 + -6x + -5x + x2 = 25 + 5x + -25 + -5x Combine like terms: -6x + -5x = -11x -20 + -11x + x2 = 25 + 5x + -25 + -5x Reorder the terms: -20 + -11x + x2 = 25 + -25 + 5x + -5x Combine like terms: 25 + -25 = 0 -20 + -11x + x2 = 0 + 5x + -5x -20 + -11x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -20 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -11x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -11x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -11x + x2 = 0 + 20 -11x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -11x + x2 = 20 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 = 20 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 20 + 30.25 Combine like terms: 20 + 30.25 = 50.25 30.25 + -11x + x2 = 50.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + -5.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + -5.5 = 7.088723439 Simplifying x + -5.5 = 7.088723439 Reorder the terms: -5.5 + x = 7.088723439 Solving -5.5 + x = 7.088723439 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 = 7.088723439 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.088723439 + 5.5 x = 7.088723439 + 5.5 Combine like terms: 7.088723439 + 5.5 = 12.588723439 x = 12.588723439 Simplifying x = 12.588723439Subproblem 2
x + -5.5 = -7.088723439 Simplifying x + -5.5 = -7.088723439 Reorder the terms: -5.5 + x = -7.088723439 Solving -5.5 + x = -7.088723439 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 = -7.088723439 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.088723439 + 5.5 x = -7.088723439 + 5.5 Combine like terms: -7.088723439 + 5.5 = -1.588723439 x = -1.588723439 Simplifying x = -1.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.588723439, -1.588723439}
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