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Simplifying 2(2x + 2)(4x + 1) = 3(3x + -4) Reorder the terms: 2(2 + 2x)(4x + 1) = 3(3x + -4) Reorder the terms: 2(2 + 2x)(1 + 4x) = 3(3x + -4) Multiply (2 + 2x) * (1 + 4x) 2(2(1 + 4x) + 2x * (1 + 4x)) = 3(3x + -4) 2((1 * 2 + 4x * 2) + 2x * (1 + 4x)) = 3(3x + -4) 2((2 + 8x) + 2x * (1 + 4x)) = 3(3x + -4) 2(2 + 8x + (1 * 2x + 4x * 2x)) = 3(3x + -4) 2(2 + 8x + (2x + 8x2)) = 3(3x + -4) Combine like terms: 8x + 2x = 10x 2(2 + 10x + 8x2) = 3(3x + -4) (2 * 2 + 10x * 2 + 8x2 * 2) = 3(3x + -4) (4 + 20x + 16x2) = 3(3x + -4) Reorder the terms: 4 + 20x + 16x2 = 3(-4 + 3x) 4 + 20x + 16x2 = (-4 * 3 + 3x * 3) 4 + 20x + 16x2 = (-12 + 9x) Solving 4 + 20x + 16x2 = -12 + 9x Solving for variable 'x'. Reorder the terms: 4 + 12 + 20x + -9x + 16x2 = -12 + 9x + 12 + -9x Combine like terms: 4 + 12 = 16 16 + 20x + -9x + 16x2 = -12 + 9x + 12 + -9x Combine like terms: 20x + -9x = 11x 16 + 11x + 16x2 = -12 + 9x + 12 + -9x Reorder the terms: 16 + 11x + 16x2 = -12 + 12 + 9x + -9x Combine like terms: -12 + 12 = 0 16 + 11x + 16x2 = 0 + 9x + -9x 16 + 11x + 16x2 = 9x + -9x Combine like terms: 9x + -9x = 0 16 + 11x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1 + 0.6875x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.6875x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 0.6875x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.6875x + x2 = 0 + -1 0.6875x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.6875x + x2 = -1 The x term is 0.6875x. Take half its coefficient (0.34375). Square it (0.1181640625) and add it to both sides. Add '0.1181640625' to each side of the equation. 0.6875x + 0.1181640625 + x2 = -1 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875x + x2 = -1 + 0.1181640625 Combine like terms: -1 + 0.1181640625 = -0.8818359375 0.1181640625 + 0.6875x + x2 = -0.8818359375 Factor a perfect square on the left side: (x + 0.34375)(x + 0.34375) = -0.8818359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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