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Simplifying 128 = 5x + -2(x + 2)(4x + 1) Reorder the terms: 128 = 5x + -2(2 + x)(4x + 1) Reorder the terms: 128 = 5x + -2(2 + x)(1 + 4x) Multiply (2 + x) * (1 + 4x) 128 = 5x + -2(2(1 + 4x) + x(1 + 4x)) 128 = 5x + -2((1 * 2 + 4x * 2) + x(1 + 4x)) 128 = 5x + -2((2 + 8x) + x(1 + 4x)) 128 = 5x + -2(2 + 8x + (1 * x + 4x * x)) 128 = 5x + -2(2 + 8x + (1x + 4x2)) Combine like terms: 8x + 1x = 9x 128 = 5x + -2(2 + 9x + 4x2) 128 = 5x + (2 * -2 + 9x * -2 + 4x2 * -2) 128 = 5x + (-4 + -18x + -8x2) Reorder the terms: 128 = -4 + 5x + -18x + -8x2 Combine like terms: 5x + -18x = -13x 128 = -4 + -13x + -8x2 Solving 128 = -4 + -13x + -8x2 Solving for variable 'x'. Combine like terms: 128 + 4 = 132 132 + 13x + 8x2 = -4 + -13x + -8x2 + 4 + 13x + 8x2 Reorder the terms: 132 + 13x + 8x2 = -4 + 4 + -13x + 13x + -8x2 + 8x2 Combine like terms: -4 + 4 = 0 132 + 13x + 8x2 = 0 + -13x + 13x + -8x2 + 8x2 132 + 13x + 8x2 = -13x + 13x + -8x2 + 8x2 Combine like terms: -13x + 13x = 0 132 + 13x + 8x2 = 0 + -8x2 + 8x2 132 + 13x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 132 + 13x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 16.5 + 1.625x + x2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + 1.625x + -16.5 + x2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + 1.625x + x2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + 1.625x + x2 = 0 + -16.5 1.625x + x2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 1.625x + x2 = -16.5 The x term is 1.625x. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625x + 0.66015625 + x2 = -16.5 + 0.66015625 Reorder the terms: 0.66015625 + 1.625x + x2 = -16.5 + 0.66015625 Combine like terms: -16.5 + 0.66015625 = -15.83984375 0.66015625 + 1.625x + x2 = -15.83984375 Factor a perfect square on the left side: (x + 0.8125)(x + 0.8125) = -15.83984375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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