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Simplifying (x + 1)(x + 1) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 Reorder the terms: (1 + x)(x + 1) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 Reorder the terms: (1 + x)(1 + x) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x)) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 ((1 * 1 + x * 1) + x(1 + x)) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 ((1 + 1x) + x(1 + x)) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 (1 + 1x + (1 * x + x * x)) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 (1 + 1x + (1x + x2)) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 Combine like terms: 1x + 1x = 2x (1 + 2x + x2) + -1(x + -2)(x + -2) + (x + 3)(x + 3) = 0 Reorder the terms: 1 + 2x + x2 + -1(-2 + x)(x + -2) + (x + 3)(x + 3) = 0 Reorder the terms: 1 + 2x + x2 + -1(-2 + x)(-2 + x) + (x + 3)(x + 3) = 0 Multiply (-2 + x) * (-2 + x) 1 + 2x + x2 + -1(-2(-2 + x) + x(-2 + x)) + (x + 3)(x + 3) = 0 1 + 2x + x2 + -1((-2 * -2 + x * -2) + x(-2 + x)) + (x + 3)(x + 3) = 0 1 + 2x + x2 + -1((4 + -2x) + x(-2 + x)) + (x + 3)(x + 3) = 0 1 + 2x + x2 + -1(4 + -2x + (-2 * x + x * x)) + (x + 3)(x + 3) = 0 1 + 2x + x2 + -1(4 + -2x + (-2x + x2)) + (x + 3)(x + 3) = 0 Combine like terms: -2x + -2x = -4x 1 + 2x + x2 + -1(4 + -4x + x2) + (x + 3)(x + 3) = 0 1 + 2x + x2 + (4 * -1 + -4x * -1 + x2 * -1) + (x + 3)(x + 3) = 0 1 + 2x + x2 + (-4 + 4x + -1x2) + (x + 3)(x + 3) = 0 Reorder the terms: 1 + 2x + x2 + -4 + 4x + -1x2 + (3 + x)(x + 3) = 0 Reorder the terms: 1 + 2x + x2 + -4 + 4x + -1x2 + (3 + x)(3 + x) = 0 Multiply (3 + x) * (3 + x) 1 + 2x + x2 + -4 + 4x + -1x2 + (3(3 + x) + x(3 + x)) = 0 1 + 2x + x2 + -4 + 4x + -1x2 + ((3 * 3 + x * 3) + x(3 + x)) = 0 1 + 2x + x2 + -4 + 4x + -1x2 + ((9 + 3x) + x(3 + x)) = 0 1 + 2x + x2 + -4 + 4x + -1x2 + (9 + 3x + (3 * x + x * x)) = 0 1 + 2x + x2 + -4 + 4x + -1x2 + (9 + 3x + (3x + x2)) = 0 Combine like terms: 3x + 3x = 6x 1 + 2x + x2 + -4 + 4x + -1x2 + (9 + 6x + x2) = 0 Reorder the terms: 1 + -4 + 9 + 2x + 4x + 6x + x2 + -1x2 + x2 = 0 Combine like terms: 1 + -4 = -3 -3 + 9 + 2x + 4x + 6x + x2 + -1x2 + x2 = 0 Combine like terms: -3 + 9 = 6 6 + 2x + 4x + 6x + x2 + -1x2 + x2 = 0 Combine like terms: 2x + 4x = 6x 6 + 6x + 6x + x2 + -1x2 + x2 = 0 Combine like terms: 6x + 6x = 12x 6 + 12x + x2 + -1x2 + x2 = 0 Combine like terms: x2 + -1x2 = 0 6 + 12x + 0 + x2 = 0 6 + 12x + x2 = 0 Solving 6 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 12x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 12x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 12x + x2 = 0 + -6 12x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 12x + x2 = -6 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -6 + 36 Reorder the terms: 36 + 12x + x2 = -6 + 36 Combine like terms: -6 + 36 = 30 36 + 12x + x2 = 30 Factor a perfect square on the left side: (x + 6)(x + 6) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 6) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 6 = 5.477225575 Simplifying x + 6 = 5.477225575 Reorder the terms: 6 + x = 5.477225575 Solving 6 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.477225575 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.477225575 + -6 x = 5.477225575 + -6 Combine like terms: 5.477225575 + -6 = -0.522774425 x = -0.522774425 Simplifying x = -0.522774425Subproblem 2
x + 6 = -5.477225575 Simplifying x + 6 = -5.477225575 Reorder the terms: 6 + x = -5.477225575 Solving 6 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.477225575 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.477225575 + -6 x = -5.477225575 + -6 Combine like terms: -5.477225575 + -6 = -11.477225575 x = -11.477225575 Simplifying x = -11.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.522774425, -11.477225575}
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