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Simplifying (6x + -4)(3x + 8) = 8 Reorder the terms: (-4 + 6x)(3x + 8) = 8 Reorder the terms: (-4 + 6x)(8 + 3x) = 8 Multiply (-4 + 6x) * (8 + 3x) (-4(8 + 3x) + 6x * (8 + 3x)) = 8 ((8 * -4 + 3x * -4) + 6x * (8 + 3x)) = 8 ((-32 + -12x) + 6x * (8 + 3x)) = 8 (-32 + -12x + (8 * 6x + 3x * 6x)) = 8 (-32 + -12x + (48x + 18x2)) = 8 Combine like terms: -12x + 48x = 36x (-32 + 36x + 18x2) = 8 Solving -32 + 36x + 18x2 = 8 Solving for variable 'x'. Reorder the terms: -32 + -8 + 36x + 18x2 = 8 + -8 Combine like terms: -32 + -8 = -40 -40 + 36x + 18x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -40 + 36x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 18x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + 18x + 9x2)' equal to zero and attempt to solve: Simplifying -20 + 18x + 9x2 = 0 Solving -20 + 18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + 2x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 2x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 2x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 2x + x2 = 0 + 2.222222222 2x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 2x + x2 = 2.222222222 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 2.222222222 + 1 Reorder the terms: 1 + 2x + x2 = 2.222222222 + 1 Combine like terms: 2.222222222 + 1 = 3.222222222 1 + 2x + x2 = 3.222222222 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.222222222 Calculate the square root of the right side: 1.795054936 Break this problem into two subproblems by setting (x + 1) equal to 1.795054936 and -1.795054936.Subproblem 1
x + 1 = 1.795054936 Simplifying x + 1 = 1.795054936 Reorder the terms: 1 + x = 1.795054936 Solving 1 + x = 1.795054936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.795054936 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.795054936 + -1 x = 1.795054936 + -1 Combine like terms: 1.795054936 + -1 = 0.795054936 x = 0.795054936 Simplifying x = 0.795054936Subproblem 2
x + 1 = -1.795054936 Simplifying x + 1 = -1.795054936 Reorder the terms: 1 + x = -1.795054936 Solving 1 + x = -1.795054936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.795054936 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.795054936 + -1 x = -1.795054936 + -1 Combine like terms: -1.795054936 + -1 = -2.795054936 x = -2.795054936 Simplifying x = -2.795054936Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.795054936, -2.795054936}Solution
x = {0.795054936, -2.795054936}
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