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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 = 1.531128874 x = 1.531128874 Simplifying x = 1.531128874Subproblem 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 = -6.531128874 x = -6.531128874 Simplifying x = -6.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.531128874, -6.531128874}
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