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Simplifying (4x + -1)(x + 2) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 Reorder the terms: (-1 + 4x)(x + 2) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 Reorder the terms: (-1 + 4x)(2 + x) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 Multiply (-1 + 4x) * (2 + x) (-1(2 + x) + 4x * (2 + x)) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 ((2 * -1 + x * -1) + 4x * (2 + x)) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 ((-2 + -1x) + 4x * (2 + x)) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 (-2 + -1x + (2 * 4x + x * 4x)) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 (-2 + -1x + (8x + 4x2)) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 Combine like terms: -1x + 8x = 7x (-2 + 7x + 4x2) + 3(2x + 7) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 Reorder the terms: -2 + 7x + 4x2 + 3(7 + 2x) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 -2 + 7x + 4x2 + (7 * 3 + 2x * 3) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 -2 + 7x + 4x2 + (21 + 6x) + -1(2x + -7) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 Reorder the terms: -2 + 7x + 4x2 + 21 + 6x + -1(-7 + 2x) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 -2 + 7x + 4x2 + 21 + 6x + (-7 * -1 + 2x * -1) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 -2 + 7x + 4x2 + 21 + 6x + (7 + -2x) + -1(3x + -7) + -4(6 + -5x)(x + 2) = 0 Reorder the terms: -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + -1(-7 + 3x) + -4(6 + -5x)(x + 2) = 0 -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + (-7 * -1 + 3x * -1) + -4(6 + -5x)(x + 2) = 0 -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + (7 + -3x) + -4(6 + -5x)(x + 2) = 0 Reorder the terms: -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + -4(6 + -5x)(2 + x) = 0 Multiply (6 + -5x) * (2 + x) -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + -4(6(2 + x) + -5x * (2 + x)) = 0 -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + -4((2 * 6 + x * 6) + -5x * (2 + x)) = 0 -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + -4((12 + 6x) + -5x * (2 + x)) = 0 -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + -4(12 + 6x + (2 * -5x + x * -5x)) = 0 -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + -4(12 + 6x + (-10x + -5x2)) = 0 Combine like terms: 6x + -10x = -4x -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + -4(12 + -4x + -5x2) = 0 -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + (12 * -4 + -4x * -4 + -5x2 * -4) = 0 -2 + 7x + 4x2 + 21 + 6x + 7 + -2x + 7 + -3x + (-48 + 16x + 20x2) = 0 Reorder the terms: -2 + 21 + 7 + 7 + -48 + 7x + 6x + -2x + -3x + 16x + 4x2 + 20x2 = 0 Combine like terms: -2 + 21 = 19 19 + 7 + 7 + -48 + 7x + 6x + -2x + -3x + 16x + 4x2 + 20x2 = 0 Combine like terms: 19 + 7 = 26 26 + 7 + -48 + 7x + 6x + -2x + -3x + 16x + 4x2 + 20x2 = 0 Combine like terms: 26 + 7 = 33 33 + -48 + 7x + 6x + -2x + -3x + 16x + 4x2 + 20x2 = 0 Combine like terms: 33 + -48 = -15 -15 + 7x + 6x + -2x + -3x + 16x + 4x2 + 20x2 = 0 Combine like terms: 7x + 6x = 13x -15 + 13x + -2x + -3x + 16x + 4x2 + 20x2 = 0 Combine like terms: 13x + -2x = 11x -15 + 11x + -3x + 16x + 4x2 + 20x2 = 0 Combine like terms: 11x + -3x = 8x -15 + 8x + 16x + 4x2 + 20x2 = 0 Combine like terms: 8x + 16x = 24x -15 + 24x + 4x2 + 20x2 = 0 Combine like terms: 4x2 + 20x2 = 24x2 -15 + 24x + 24x2 = 0 Solving -15 + 24x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 8x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 8x + 8x2)' equal to zero and attempt to solve: Simplifying -5 + 8x + 8x2 = 0 Solving -5 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x + x2 = 0 + 0.625 x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 x + x2 = 0.625 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.625 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.625 + 0.25 Combine like terms: 0.625 + 0.25 = 0.875 1.25 + x2 = 0.875 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (x + 0.5) equal to 0.935414347 and -0.935414347.Subproblem 1
x + 0.5 = 0.935414347 Simplifying x + 0.5 = 0.935414347 Reorder the terms: 0.5 + x = 0.935414347 Solving 0.5 + x = 0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.935414347 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.935414347 + -0.5 x = 0.935414347 + -0.5 Combine like terms: 0.935414347 + -0.5 = 0.435414347 x = 0.435414347 Simplifying x = 0.435414347Subproblem 2
x + 0.5 = -0.935414347 Simplifying x + 0.5 = -0.935414347 Reorder the terms: 0.5 + x = -0.935414347 Solving 0.5 + x = -0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.935414347 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.935414347 + -0.5 x = -0.935414347 + -0.5 Combine like terms: -0.935414347 + -0.5 = -1.435414347 x = -1.435414347 Simplifying x = -1.435414347Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.435414347, -1.435414347}Solution
x = {0.435414347, -1.435414347}
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