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Simplifying (x + 1)(x + 4) = -1 Reorder the terms: (1 + x)(x + 4) = -1 Reorder the terms: (1 + x)(4 + x) = -1 Multiply (1 + x) * (4 + x) (1(4 + x) + x(4 + x)) = -1 ((4 * 1 + x * 1) + x(4 + x)) = -1 ((4 + 1x) + x(4 + x)) = -1 (4 + 1x + (4 * x + x * x)) = -1 (4 + 1x + (4x + x2)) = -1 Combine like terms: 1x + 4x = 5x (4 + 5x + x2) = -1 Solving 4 + 5x + x2 = -1 Solving for variable 'x'. Reorder the terms: 4 + 1 + 5x + x2 = -1 + 1 Combine like terms: 4 + 1 = 5 5 + 5x + x2 = -1 + 1 Combine like terms: -1 + 1 = 0 5 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5x + x2 = 0 + -5 5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 5x + x2 = -5 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 = -5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + 5x + x2 = 1.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 2.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 2.5 = 1.118033989 Simplifying x + 2.5 = 1.118033989 Reorder the terms: 2.5 + x = 1.118033989 Solving 2.5 + x = 1.118033989 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 = 1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.118033989 + -2.5 x = 1.118033989 + -2.5 Combine like terms: 1.118033989 + -2.5 = -1.381966011 x = -1.381966011 Simplifying x = -1.381966011Subproblem 2
x + 2.5 = -1.118033989 Simplifying x + 2.5 = -1.118033989 Reorder the terms: 2.5 + x = -1.118033989 Solving 2.5 + x = -1.118033989 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 = -1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.118033989 + -2.5 x = -1.118033989 + -2.5 Combine like terms: -1.118033989 + -2.5 = -3.618033989 x = -3.618033989 Simplifying x = -3.618033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.381966011, -3.618033989}
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