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Simplifying (x + -1)(x + -4) = 14 Reorder the terms: (-1 + x)(x + -4) = 14 Reorder the terms: (-1 + x)(-4 + x) = 14 Multiply (-1 + x) * (-4 + x) (-1(-4 + x) + x(-4 + x)) = 14 ((-4 * -1 + x * -1) + x(-4 + x)) = 14 ((4 + -1x) + x(-4 + x)) = 14 (4 + -1x + (-4 * x + x * x)) = 14 (4 + -1x + (-4x + x2)) = 14 Combine like terms: -1x + -4x = -5x (4 + -5x + x2) = 14 Solving 4 + -5x + x2 = 14 Solving for variable 'x'. Reorder the terms: 4 + -14 + -5x + x2 = 14 + -14 Combine like terms: 4 + -14 = -10 -10 + -5x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -10 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5x + x2 = 0 + 10 -5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5x + x2 = 10 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 = 10 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 10 + 6.25 Combine like terms: 10 + 6.25 = 16.25 6.25 + -5x + x2 = 16.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -2.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -2.5 = 4.031128874 Simplifying x + -2.5 = 4.031128874 Reorder the terms: -2.5 + x = 4.031128874 Solving -2.5 + x = 4.031128874 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 = 4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.031128874 + 2.5 x = 4.031128874 + 2.5 Combine like terms: 4.031128874 + 2.5 = 6.531128874 x = 6.531128874 Simplifying x = 6.531128874Subproblem 2
x + -2.5 = -4.031128874 Simplifying x + -2.5 = -4.031128874 Reorder the terms: -2.5 + x = -4.031128874 Solving -2.5 + x = -4.031128874 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 = -4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.031128874 + 2.5 x = -4.031128874 + 2.5 Combine like terms: -4.031128874 + 2.5 = -1.531128874 x = -1.531128874 Simplifying x = -1.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.531128874, -1.531128874}
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