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Simplifying x(x + 2) + 2 = -4(x + 1) Reorder the terms: x(2 + x) + 2 = -4(x + 1) (2 * x + x * x) + 2 = -4(x + 1) (2x + x2) + 2 = -4(x + 1) Reorder the terms: 2 + 2x + x2 = -4(x + 1) Reorder the terms: 2 + 2x + x2 = -4(1 + x) 2 + 2x + x2 = (1 * -4 + x * -4) 2 + 2x + x2 = (-4 + -4x) Solving 2 + 2x + x2 = -4 + -4x Solving for variable 'x'. Reorder the terms: 2 + 4 + 2x + 4x + x2 = -4 + -4x + 4 + 4x Combine like terms: 2 + 4 = 6 6 + 2x + 4x + x2 = -4 + -4x + 4 + 4x Combine like terms: 2x + 4x = 6x 6 + 6x + x2 = -4 + -4x + 4 + 4x Reorder the terms: 6 + 6x + x2 = -4 + 4 + -4x + 4x Combine like terms: -4 + 4 = 0 6 + 6x + x2 = 0 + -4x + 4x 6 + 6x + x2 = -4x + 4x Combine like terms: -4x + 4x = 0 6 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 6x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 6x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6x + x2 = 0 + -6 6x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 6x + x2 = -6 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -6 + 9 Reorder the terms: 9 + 6x + x2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + 6x + x2 = 3 Factor a perfect square on the left side: (x + 3)(x + 3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 3) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 3 = 1.732050808 Simplifying x + 3 = 1.732050808 Reorder the terms: 3 + x = 1.732050808 Solving 3 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.732050808 + -3 x = 1.732050808 + -3 Combine like terms: 1.732050808 + -3 = -1.267949192 x = -1.267949192 Simplifying x = -1.267949192Subproblem 2
x + 3 = -1.732050808 Simplifying x + 3 = -1.732050808 Reorder the terms: 3 + x = -1.732050808 Solving 3 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.732050808 + -3 x = -1.732050808 + -3 Combine like terms: -1.732050808 + -3 = -4.732050808 x = -4.732050808 Simplifying x = -4.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.267949192, -4.732050808}
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