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Simplifying 5(x + 2) + -1(x + -1)(x + 4) + -6x = 0 Reorder the terms: 5(2 + x) + -1(x + -1)(x + 4) + -6x = 0 (2 * 5 + x * 5) + -1(x + -1)(x + 4) + -6x = 0 (10 + 5x) + -1(x + -1)(x + 4) + -6x = 0 Reorder the terms: 10 + 5x + -1(-1 + x)(x + 4) + -6x = 0 Reorder the terms: 10 + 5x + -1(-1 + x)(4 + x) + -6x = 0 Multiply (-1 + x) * (4 + x) 10 + 5x + -1(-1(4 + x) + x(4 + x)) + -6x = 0 10 + 5x + -1((4 * -1 + x * -1) + x(4 + x)) + -6x = 0 10 + 5x + -1((-4 + -1x) + x(4 + x)) + -6x = 0 10 + 5x + -1(-4 + -1x + (4 * x + x * x)) + -6x = 0 10 + 5x + -1(-4 + -1x + (4x + x2)) + -6x = 0 Combine like terms: -1x + 4x = 3x 10 + 5x + -1(-4 + 3x + x2) + -6x = 0 10 + 5x + (-4 * -1 + 3x * -1 + x2 * -1) + -6x = 0 10 + 5x + (4 + -3x + -1x2) + -6x = 0 Reorder the terms: 10 + 4 + 5x + -3x + -6x + -1x2 = 0 Combine like terms: 10 + 4 = 14 14 + 5x + -3x + -6x + -1x2 = 0 Combine like terms: 5x + -3x = 2x 14 + 2x + -6x + -1x2 = 0 Combine like terms: 2x + -6x = -4x 14 + -4x + -1x2 = 0 Solving 14 + -4x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 4x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 4x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 4x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 4x + x2 = 0 + 14 4x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 4x + x2 = 14 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 = 14 + 4 Reorder the terms: 4 + 4x + x2 = 14 + 4 Combine like terms: 14 + 4 = 18 4 + 4x + x2 = 18 Factor a perfect square on the left side: (x + 2)(x + 2) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 2) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 2 = 4.242640687 Simplifying x + 2 = 4.242640687 Reorder the terms: 2 + x = 4.242640687 Solving 2 + x = 4.242640687 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 = 4.242640687 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.242640687 + -2 x = 4.242640687 + -2 Combine like terms: 4.242640687 + -2 = 2.242640687 x = 2.242640687 Simplifying x = 2.242640687Subproblem 2
x + 2 = -4.242640687 Simplifying x + 2 = -4.242640687 Reorder the terms: 2 + x = -4.242640687 Solving 2 + x = -4.242640687 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 = -4.242640687 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.242640687 + -2 x = -4.242640687 + -2 Combine like terms: -4.242640687 + -2 = -6.242640687 x = -6.242640687 Simplifying x = -6.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.242640687, -6.242640687}
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