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Simplifying 4x2 + -16x + 24 = -2x + 9 Reorder the terms: 24 + -16x + 4x2 = -2x + 9 Reorder the terms: 24 + -16x + 4x2 = 9 + -2x Solving 24 + -16x + 4x2 = 9 + -2x Solving for variable 'x'. Reorder the terms: 24 + -9 + -16x + 2x + 4x2 = 9 + -2x + -9 + 2x Combine like terms: 24 + -9 = 15 15 + -16x + 2x + 4x2 = 9 + -2x + -9 + 2x Combine like terms: -16x + 2x = -14x 15 + -14x + 4x2 = 9 + -2x + -9 + 2x Reorder the terms: 15 + -14x + 4x2 = 9 + -9 + -2x + 2x Combine like terms: 9 + -9 = 0 15 + -14x + 4x2 = 0 + -2x + 2x 15 + -14x + 4x2 = -2x + 2x Combine like terms: -2x + 2x = 0 15 + -14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -3.5x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -3.5x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -3.5x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -3.5x + x2 = 0 + -3.75 -3.5x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -3.5x + x2 = -3.75 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -3.75 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -3.75 + 3.0625 Combine like terms: -3.75 + 3.0625 = -0.6875 3.0625 + -3.5x + x2 = -0.6875 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -0.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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