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Simplifying 3x + (x + 4)(x + 1) = 0 Reorder the terms: 3x + (4 + x)(x + 1) = 0 Reorder the terms: 3x + (4 + x)(1 + x) = 0 Multiply (4 + x) * (1 + x) 3x + (4(1 + x) + x(1 + x)) = 0 3x + ((1 * 4 + x * 4) + x(1 + x)) = 0 3x + ((4 + 4x) + x(1 + x)) = 0 3x + (4 + 4x + (1 * x + x * x)) = 0 3x + (4 + 4x + (1x + x2)) = 0 Combine like terms: 4x + 1x = 5x 3x + (4 + 5x + x2) = 0 Reorder the terms: 4 + 3x + 5x + x2 = 0 Combine like terms: 3x + 5x = 8x 4 + 8x + x2 = 0 Solving 4 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 8x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 8x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8x + x2 = 0 + -4 8x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 8x + x2 = -4 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -4 + 16 Reorder the terms: 16 + 8x + x2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + 8x + x2 = 12 Factor a perfect square on the left side: (x + 4)(x + 4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 4) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 4 = 3.464101615 Simplifying x + 4 = 3.464101615 Reorder the terms: 4 + x = 3.464101615 Solving 4 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.464101615 + -4 x = 3.464101615 + -4 Combine like terms: 3.464101615 + -4 = -0.535898385 x = -0.535898385 Simplifying x = -0.535898385Subproblem 2
x + 4 = -3.464101615 Simplifying x + 4 = -3.464101615 Reorder the terms: 4 + x = -3.464101615 Solving 4 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.464101615 + -4 x = -3.464101615 + -4 Combine like terms: -3.464101615 + -4 = -7.464101615 x = -7.464101615 Simplifying x = -7.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.535898385, -7.464101615}
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