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Simplifying (x + 4)(2x + 1) = x Reorder the terms: (4 + x)(2x + 1) = x Reorder the terms: (4 + x)(1 + 2x) = x Multiply (4 + x) * (1 + 2x) (4(1 + 2x) + x(1 + 2x)) = x ((1 * 4 + 2x * 4) + x(1 + 2x)) = x ((4 + 8x) + x(1 + 2x)) = x (4 + 8x + (1 * x + 2x * x)) = x (4 + 8x + (1x + 2x2)) = x Combine like terms: 8x + 1x = 9x (4 + 9x + 2x2) = x Solving 4 + 9x + 2x2 = x Solving for variable 'x'. Reorder the terms: 4 + 9x + -1x + 2x2 = x + -1x Combine like terms: 9x + -1x = 8x 4 + 8x + 2x2 = x + -1x Combine like terms: x + -1x = 0 4 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 4x + x2)' equal to zero and attempt to solve: Simplifying 2 + 4x + x2 = 0 Solving 2 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4x + x2 = 0 + -2 4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 4x + x2 = -2 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2 + 4 Reorder the terms: 4 + 4x + x2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + 4x + x2 = 2 Factor a perfect square on the left side: (x + 2)(x + 2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 2) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 2 = 1.414213562 Simplifying x + 2 = 1.414213562 Reorder the terms: 2 + x = 1.414213562 Solving 2 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.414213562 + -2 x = 1.414213562 + -2 Combine like terms: 1.414213562 + -2 = -0.585786438 x = -0.585786438 Simplifying x = -0.585786438Subproblem 2
x + 2 = -1.414213562 Simplifying x + 2 = -1.414213562 Reorder the terms: 2 + x = -1.414213562 Solving 2 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.414213562 + -2 x = -1.414213562 + -2 Combine like terms: -1.414213562 + -2 = -3.414213562 x = -3.414213562 Simplifying x = -3.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.585786438, -3.414213562}Solution
x = {-0.585786438, -3.414213562}
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