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Simplifying (2X + -3)(X + 4) = 4X + -43 Reorder the terms: (-3 + 2X)(X + 4) = 4X + -43 Reorder the terms: (-3 + 2X)(4 + X) = 4X + -43 Multiply (-3 + 2X) * (4 + X) (-3(4 + X) + 2X * (4 + X)) = 4X + -43 ((4 * -3 + X * -3) + 2X * (4 + X)) = 4X + -43 ((-12 + -3X) + 2X * (4 + X)) = 4X + -43 (-12 + -3X + (4 * 2X + X * 2X)) = 4X + -43 (-12 + -3X + (8X + 2X2)) = 4X + -43 Combine like terms: -3X + 8X = 5X (-12 + 5X + 2X2) = 4X + -43 Reorder the terms: -12 + 5X + 2X2 = -43 + 4X Solving -12 + 5X + 2X2 = -43 + 4X Solving for variable 'X'. Reorder the terms: -12 + 43 + 5X + -4X + 2X2 = -43 + 4X + 43 + -4X Combine like terms: -12 + 43 = 31 31 + 5X + -4X + 2X2 = -43 + 4X + 43 + -4X Combine like terms: 5X + -4X = 1X 31 + 1X + 2X2 = -43 + 4X + 43 + -4X Reorder the terms: 31 + 1X + 2X2 = -43 + 43 + 4X + -4X Combine like terms: -43 + 43 = 0 31 + 1X + 2X2 = 0 + 4X + -4X 31 + 1X + 2X2 = 4X + -4X Combine like terms: 4X + -4X = 0 31 + 1X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15.5 + 0.5X + X2 = 0 Move the constant term to the right: Add '-15.5' to each side of the equation. 15.5 + 0.5X + -15.5 + X2 = 0 + -15.5 Reorder the terms: 15.5 + -15.5 + 0.5X + X2 = 0 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + 0.5X + X2 = 0 + -15.5 0.5X + X2 = 0 + -15.5 Combine like terms: 0 + -15.5 = -15.5 0.5X + X2 = -15.5 The X term is 0.5X. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5X + 0.0625 + X2 = -15.5 + 0.0625 Reorder the terms: 0.0625 + 0.5X + X2 = -15.5 + 0.0625 Combine like terms: -15.5 + 0.0625 = -15.4375 0.0625 + 0.5X + X2 = -15.4375 Factor a perfect square on the left side: (X + 0.25)(X + 0.25) = -15.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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