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Simplifying 8x + -23 = x2 + 2x + 1 Reorder the terms: -23 + 8x = x2 + 2x + 1 Reorder the terms: -23 + 8x = 1 + 2x + x2 Solving -23 + 8x = 1 + 2x + x2 Solving for variable 'x'. Reorder the terms: -23 + -1 + 8x + -2x + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Combine like terms: -23 + -1 = -24 -24 + 8x + -2x + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Combine like terms: 8x + -2x = 6x -24 + 6x + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Reorder the terms: -24 + 6x + -1x2 = 1 + -1 + 2x + -2x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -24 + 6x + -1x2 = 0 + 2x + -2x + x2 + -1x2 -24 + 6x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -24 + 6x + -1x2 = 0 + x2 + -1x2 -24 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -24 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -6x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -6x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -6x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -6x + x2 = 0 + -24 -6x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -6x + x2 = -24 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -24 + 9 Reorder the terms: 9 + -6x + x2 = -24 + 9 Combine like terms: -24 + 9 = -15 9 + -6x + x2 = -15 Factor a perfect square on the left side: (x + -3)(x + -3) = -15 Can't calculate square root of the right side. The solution to this equation could not be determined.
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