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Simplifying (14)(3x + 3) = (4x + 4)(4x + 4) Reorder the terms: 14(3 + 3x) = (4x + 4)(4x + 4) (3 * 14 + 3x * 14) = (4x + 4)(4x + 4) (42 + 42x) = (4x + 4)(4x + 4) Reorder the terms: 42 + 42x = (4 + 4x)(4x + 4) Reorder the terms: 42 + 42x = (4 + 4x)(4 + 4x) Multiply (4 + 4x) * (4 + 4x) 42 + 42x = (4(4 + 4x) + 4x * (4 + 4x)) 42 + 42x = ((4 * 4 + 4x * 4) + 4x * (4 + 4x)) 42 + 42x = ((16 + 16x) + 4x * (4 + 4x)) 42 + 42x = (16 + 16x + (4 * 4x + 4x * 4x)) 42 + 42x = (16 + 16x + (16x + 16x2)) Combine like terms: 16x + 16x = 32x 42 + 42x = (16 + 32x + 16x2) Solving 42 + 42x = 16 + 32x + 16x2 Solving for variable 'x'. Reorder the terms: 42 + -16 + 42x + -32x + -16x2 = 16 + 32x + 16x2 + -16 + -32x + -16x2 Combine like terms: 42 + -16 = 26 26 + 42x + -32x + -16x2 = 16 + 32x + 16x2 + -16 + -32x + -16x2 Combine like terms: 42x + -32x = 10x 26 + 10x + -16x2 = 16 + 32x + 16x2 + -16 + -32x + -16x2 Reorder the terms: 26 + 10x + -16x2 = 16 + -16 + 32x + -32x + 16x2 + -16x2 Combine like terms: 16 + -16 = 0 26 + 10x + -16x2 = 0 + 32x + -32x + 16x2 + -16x2 26 + 10x + -16x2 = 32x + -32x + 16x2 + -16x2 Combine like terms: 32x + -32x = 0 26 + 10x + -16x2 = 0 + 16x2 + -16x2 26 + 10x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 26 + 10x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + 5x + -8x2) = 0 Factor a trinomial. 2((13 + -8x)(1 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -8x)' equal to zero and attempt to solve: Simplifying 13 + -8x = 0 Solving 13 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -8x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8x = 0 + -13 -8x = 0 + -13 Combine like terms: 0 + -13 = -13 -8x = -13 Divide each side by '-8'. x = 1.625 Simplifying x = 1.625Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 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 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {1.625, -1}
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