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Simplifying 8x(x + -1) + (3x + 5)(5x + -1) = 3(3x + 5)(x + 1) Reorder the terms: 8x(-1 + x) + (3x + 5)(5x + -1) = 3(3x + 5)(x + 1) (-1 * 8x + x * 8x) + (3x + 5)(5x + -1) = 3(3x + 5)(x + 1) (-8x + 8x2) + (3x + 5)(5x + -1) = 3(3x + 5)(x + 1) Reorder the terms: -8x + 8x2 + (5 + 3x)(5x + -1) = 3(3x + 5)(x + 1) Reorder the terms: -8x + 8x2 + (5 + 3x)(-1 + 5x) = 3(3x + 5)(x + 1) Multiply (5 + 3x) * (-1 + 5x) -8x + 8x2 + (5(-1 + 5x) + 3x * (-1 + 5x)) = 3(3x + 5)(x + 1) -8x + 8x2 + ((-1 * 5 + 5x * 5) + 3x * (-1 + 5x)) = 3(3x + 5)(x + 1) -8x + 8x2 + ((-5 + 25x) + 3x * (-1 + 5x)) = 3(3x + 5)(x + 1) -8x + 8x2 + (-5 + 25x + (-1 * 3x + 5x * 3x)) = 3(3x + 5)(x + 1) -8x + 8x2 + (-5 + 25x + (-3x + 15x2)) = 3(3x + 5)(x + 1) Combine like terms: 25x + -3x = 22x -8x + 8x2 + (-5 + 22x + 15x2) = 3(3x + 5)(x + 1) Reorder the terms: -5 + -8x + 22x + 8x2 + 15x2 = 3(3x + 5)(x + 1) Combine like terms: -8x + 22x = 14x -5 + 14x + 8x2 + 15x2 = 3(3x + 5)(x + 1) Combine like terms: 8x2 + 15x2 = 23x2 -5 + 14x + 23x2 = 3(3x + 5)(x + 1) Reorder the terms: -5 + 14x + 23x2 = 3(5 + 3x)(x + 1) Reorder the terms: -5 + 14x + 23x2 = 3(5 + 3x)(1 + x) Multiply (5 + 3x) * (1 + x) -5 + 14x + 23x2 = 3(5(1 + x) + 3x * (1 + x)) -5 + 14x + 23x2 = 3((1 * 5 + x * 5) + 3x * (1 + x)) -5 + 14x + 23x2 = 3((5 + 5x) + 3x * (1 + x)) -5 + 14x + 23x2 = 3(5 + 5x + (1 * 3x + x * 3x)) -5 + 14x + 23x2 = 3(5 + 5x + (3x + 3x2)) Combine like terms: 5x + 3x = 8x -5 + 14x + 23x2 = 3(5 + 8x + 3x2) -5 + 14x + 23x2 = (5 * 3 + 8x * 3 + 3x2 * 3) -5 + 14x + 23x2 = (15 + 24x + 9x2) Solving -5 + 14x + 23x2 = 15 + 24x + 9x2 Solving for variable 'x'. Reorder the terms: -5 + -15 + 14x + -24x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2 Combine like terms: -5 + -15 = -20 -20 + 14x + -24x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2 Combine like terms: 14x + -24x = -10x -20 + -10x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2 Combine like terms: 23x2 + -9x2 = 14x2 -20 + -10x + 14x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2 Reorder the terms: -20 + -10x + 14x2 = 15 + -15 + 24x + -24x + 9x2 + -9x2 Combine like terms: 15 + -15 = 0 -20 + -10x + 14x2 = 0 + 24x + -24x + 9x2 + -9x2 -20 + -10x + 14x2 = 24x + -24x + 9x2 + -9x2 Combine like terms: 24x + -24x = 0 -20 + -10x + 14x2 = 0 + 9x2 + -9x2 -20 + -10x + 14x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -20 + -10x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -5x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -5x + 7x2)' equal to zero and attempt to solve: Simplifying -10 + -5x + 7x2 = 0 Solving -10 + -5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.7142857143x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.7142857143x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 1.428571429 -0.7142857143x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.7142857143x + x2 = 1.428571429 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 1.428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 1.428571429 + 0.1275510204 Combine like terms: 1.428571429 + 0.1275510204 = 1.5561224494 0.1275510204 + -0.7142857143x + x2 = 1.5561224494 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 1.5561224494 Calculate the square root of the right side: 1.247446371 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.247446371 and -1.247446371.Subproblem 1
x + -0.3571428572 = 1.247446371 Simplifying x + -0.3571428572 = 1.247446371 Reorder the terms: -0.3571428572 + x = 1.247446371 Solving -0.3571428572 + x = 1.247446371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.247446371 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.247446371 + 0.3571428572 x = 1.247446371 + 0.3571428572 Combine like terms: 1.247446371 + 0.3571428572 = 1.6045892282 x = 1.6045892282 Simplifying x = 1.6045892282Subproblem 2
x + -0.3571428572 = -1.247446371 Simplifying x + -0.3571428572 = -1.247446371 Reorder the terms: -0.3571428572 + x = -1.247446371 Solving -0.3571428572 + x = -1.247446371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.247446371 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.247446371 + 0.3571428572 x = -1.247446371 + 0.3571428572 Combine like terms: -1.247446371 + 0.3571428572 = -0.8903035138 x = -0.8903035138 Simplifying x = -0.8903035138Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6045892282, -0.8903035138}Solution
x = {1.6045892282, -0.8903035138}
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