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Simplifying 5x(x + -1) + 16(2x + 3) = 3(2x + -7) + -1x Reorder the terms: 5x(-1 + x) + 16(2x + 3) = 3(2x + -7) + -1x (-1 * 5x + x * 5x) + 16(2x + 3) = 3(2x + -7) + -1x (-5x + 5x2) + 16(2x + 3) = 3(2x + -7) + -1x Reorder the terms: -5x + 5x2 + 16(3 + 2x) = 3(2x + -7) + -1x -5x + 5x2 + (3 * 16 + 2x * 16) = 3(2x + -7) + -1x -5x + 5x2 + (48 + 32x) = 3(2x + -7) + -1x Reorder the terms: 48 + -5x + 32x + 5x2 = 3(2x + -7) + -1x Combine like terms: -5x + 32x = 27x 48 + 27x + 5x2 = 3(2x + -7) + -1x Reorder the terms: 48 + 27x + 5x2 = 3(-7 + 2x) + -1x 48 + 27x + 5x2 = (-7 * 3 + 2x * 3) + -1x 48 + 27x + 5x2 = (-21 + 6x) + -1x Combine like terms: 6x + -1x = 5x 48 + 27x + 5x2 = -21 + 5x Solving 48 + 27x + 5x2 = -21 + 5x Solving for variable 'x'. Reorder the terms: 48 + 21 + 27x + -5x + 5x2 = -21 + 5x + 21 + -5x Combine like terms: 48 + 21 = 69 69 + 27x + -5x + 5x2 = -21 + 5x + 21 + -5x Combine like terms: 27x + -5x = 22x 69 + 22x + 5x2 = -21 + 5x + 21 + -5x Reorder the terms: 69 + 22x + 5x2 = -21 + 21 + 5x + -5x Combine like terms: -21 + 21 = 0 69 + 22x + 5x2 = 0 + 5x + -5x 69 + 22x + 5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 69 + 22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 13.8 + 4.4x + x2 = 0 Move the constant term to the right: Add '-13.8' to each side of the equation. 13.8 + 4.4x + -13.8 + x2 = 0 + -13.8 Reorder the terms: 13.8 + -13.8 + 4.4x + x2 = 0 + -13.8 Combine like terms: 13.8 + -13.8 = 0.0 0.0 + 4.4x + x2 = 0 + -13.8 4.4x + x2 = 0 + -13.8 Combine like terms: 0 + -13.8 = -13.8 4.4x + x2 = -13.8 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = -13.8 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = -13.8 + 4.84 Combine like terms: -13.8 + 4.84 = -8.96 4.84 + 4.4x + x2 = -8.96 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = -8.96 Can't calculate square root of the right side. The solution to this equation could not be determined.
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