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Simplifying 2(x + 1)(x + 4) + -1(x + -2)(x + -2) = 0 Reorder the terms: 2(1 + x)(x + 4) + -1(x + -2)(x + -2) = 0 Reorder the terms: 2(1 + x)(4 + x) + -1(x + -2)(x + -2) = 0 Multiply (1 + x) * (4 + x) 2(1(4 + x) + x(4 + x)) + -1(x + -2)(x + -2) = 0 2((4 * 1 + x * 1) + x(4 + x)) + -1(x + -2)(x + -2) = 0 2((4 + 1x) + x(4 + x)) + -1(x + -2)(x + -2) = 0 2(4 + 1x + (4 * x + x * x)) + -1(x + -2)(x + -2) = 0 2(4 + 1x + (4x + x2)) + -1(x + -2)(x + -2) = 0 Combine like terms: 1x + 4x = 5x 2(4 + 5x + x2) + -1(x + -2)(x + -2) = 0 (4 * 2 + 5x * 2 + x2 * 2) + -1(x + -2)(x + -2) = 0 (8 + 10x + 2x2) + -1(x + -2)(x + -2) = 0 Reorder the terms: 8 + 10x + 2x2 + -1(-2 + x)(x + -2) = 0 Reorder the terms: 8 + 10x + 2x2 + -1(-2 + x)(-2 + x) = 0 Multiply (-2 + x) * (-2 + x) 8 + 10x + 2x2 + -1(-2(-2 + x) + x(-2 + x)) = 0 8 + 10x + 2x2 + -1((-2 * -2 + x * -2) + x(-2 + x)) = 0 8 + 10x + 2x2 + -1((4 + -2x) + x(-2 + x)) = 0 8 + 10x + 2x2 + -1(4 + -2x + (-2 * x + x * x)) = 0 8 + 10x + 2x2 + -1(4 + -2x + (-2x + x2)) = 0 Combine like terms: -2x + -2x = -4x 8 + 10x + 2x2 + -1(4 + -4x + x2) = 0 8 + 10x + 2x2 + (4 * -1 + -4x * -1 + x2 * -1) = 0 8 + 10x + 2x2 + (-4 + 4x + -1x2) = 0 Reorder the terms: 8 + -4 + 10x + 4x + 2x2 + -1x2 = 0 Combine like terms: 8 + -4 = 4 4 + 10x + 4x + 2x2 + -1x2 = 0 Combine like terms: 10x + 4x = 14x 4 + 14x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 4 + 14x + 1x2 = 0 Solving 4 + 14x + 1x2 = 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 + 14x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 14x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 14x + x2 = 0 + -4 14x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 14x + x2 = -4 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -4 + 49 Reorder the terms: 49 + 14x + x2 = -4 + 49 Combine like terms: -4 + 49 = 45 49 + 14x + x2 = 45 Factor a perfect square on the left side: (x + 7)(x + 7) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 7) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 7 = 6.708203933 Simplifying x + 7 = 6.708203933 Reorder the terms: 7 + x = 6.708203933 Solving 7 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 6.708203933 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.708203933 + -7 x = 6.708203933 + -7 Combine like terms: 6.708203933 + -7 = -0.291796067 x = -0.291796067 Simplifying x = -0.291796067Subproblem 2
x + 7 = -6.708203933 Simplifying x + 7 = -6.708203933 Reorder the terms: 7 + x = -6.708203933 Solving 7 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -6.708203933 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.708203933 + -7 x = -6.708203933 + -7 Combine like terms: -6.708203933 + -7 = -13.708203933 x = -13.708203933 Simplifying x = -13.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.291796067, -13.708203933}
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