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Simplifying (6x + 2)(8x + -14) = (14x + -12) Reorder the terms: (2 + 6x)(8x + -14) = (14x + -12) Reorder the terms: (2 + 6x)(-14 + 8x) = (14x + -12) Multiply (2 + 6x) * (-14 + 8x) (2(-14 + 8x) + 6x * (-14 + 8x)) = (14x + -12) ((-14 * 2 + 8x * 2) + 6x * (-14 + 8x)) = (14x + -12) ((-28 + 16x) + 6x * (-14 + 8x)) = (14x + -12) (-28 + 16x + (-14 * 6x + 8x * 6x)) = (14x + -12) (-28 + 16x + (-84x + 48x2)) = (14x + -12) Combine like terms: 16x + -84x = -68x (-28 + -68x + 48x2) = (14x + -12) Reorder the terms: -28 + -68x + 48x2 = (-12 + 14x) Remove parenthesis around (-12 + 14x) -28 + -68x + 48x2 = -12 + 14x Solving -28 + -68x + 48x2 = -12 + 14x Solving for variable 'x'. Reorder the terms: -28 + 12 + -68x + -14x + 48x2 = -12 + 14x + 12 + -14x Combine like terms: -28 + 12 = -16 -16 + -68x + -14x + 48x2 = -12 + 14x + 12 + -14x Combine like terms: -68x + -14x = -82x -16 + -82x + 48x2 = -12 + 14x + 12 + -14x Reorder the terms: -16 + -82x + 48x2 = -12 + 12 + 14x + -14x Combine like terms: -12 + 12 = 0 -16 + -82x + 48x2 = 0 + 14x + -14x -16 + -82x + 48x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -16 + -82x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -41x + 24x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -41x + 24x2)' equal to zero and attempt to solve: Simplifying -8 + -41x + 24x2 = 0 Solving -8 + -41x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.3333333333 + -1.708333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.708333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.708333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.708333333x + x2 = 0 + 0.3333333333 -1.708333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.708333333x + x2 = 0.3333333333 The x term is -1.708333333x. Take half its coefficient (-0.8541666665). Square it (0.7296006942) and add it to both sides. Add '0.7296006942' to each side of the equation. -1.708333333x + 0.7296006942 + x2 = 0.3333333333 + 0.7296006942 Reorder the terms: 0.7296006942 + -1.708333333x + x2 = 0.3333333333 + 0.7296006942 Combine like terms: 0.3333333333 + 0.7296006942 = 1.0629340275 0.7296006942 + -1.708333333x + x2 = 1.0629340275 Factor a perfect square on the left side: (x + -0.8541666665)(x + -0.8541666665) = 1.0629340275 Calculate the square root of the right side: 1.030986919 Break this problem into two subproblems by setting (x + -0.8541666665) equal to 1.030986919 and -1.030986919.Subproblem 1
x + -0.8541666665 = 1.030986919 Simplifying x + -0.8541666665 = 1.030986919 Reorder the terms: -0.8541666665 + x = 1.030986919 Solving -0.8541666665 + x = 1.030986919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8541666665' to each side of the equation. -0.8541666665 + 0.8541666665 + x = 1.030986919 + 0.8541666665 Combine like terms: -0.8541666665 + 0.8541666665 = 0.0000000000 0.0000000000 + x = 1.030986919 + 0.8541666665 x = 1.030986919 + 0.8541666665 Combine like terms: 1.030986919 + 0.8541666665 = 1.8851535855 x = 1.8851535855 Simplifying x = 1.8851535855Subproblem 2
x + -0.8541666665 = -1.030986919 Simplifying x + -0.8541666665 = -1.030986919 Reorder the terms: -0.8541666665 + x = -1.030986919 Solving -0.8541666665 + x = -1.030986919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8541666665' to each side of the equation. -0.8541666665 + 0.8541666665 + x = -1.030986919 + 0.8541666665 Combine like terms: -0.8541666665 + 0.8541666665 = 0.0000000000 0.0000000000 + x = -1.030986919 + 0.8541666665 x = -1.030986919 + 0.8541666665 Combine like terms: -1.030986919 + 0.8541666665 = -0.1768202525 x = -0.1768202525 Simplifying x = -0.1768202525Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8851535855, -0.1768202525}Solution
x = {1.8851535855, -0.1768202525}
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