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Simplifying 2x + 6 = -1x2 + 10x + -27 Reorder the terms: 6 + 2x = -1x2 + 10x + -27 Reorder the terms: 6 + 2x = -27 + 10x + -1x2 Solving 6 + 2x = -27 + 10x + -1x2 Solving for variable 'x'. Reorder the terms: 6 + 27 + 2x + -10x + x2 = -27 + 10x + -1x2 + 27 + -10x + x2 Combine like terms: 6 + 27 = 33 33 + 2x + -10x + x2 = -27 + 10x + -1x2 + 27 + -10x + x2 Combine like terms: 2x + -10x = -8x 33 + -8x + x2 = -27 + 10x + -1x2 + 27 + -10x + x2 Reorder the terms: 33 + -8x + x2 = -27 + 27 + 10x + -10x + -1x2 + x2 Combine like terms: -27 + 27 = 0 33 + -8x + x2 = 0 + 10x + -10x + -1x2 + x2 33 + -8x + x2 = 10x + -10x + -1x2 + x2 Combine like terms: 10x + -10x = 0 33 + -8x + x2 = 0 + -1x2 + x2 33 + -8x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 33 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -8x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + -8x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -8x + x2 = 0 + -33 -8x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 -8x + x2 = -33 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -33 + 16 Reorder the terms: 16 + -8x + x2 = -33 + 16 Combine like terms: -33 + 16 = -17 16 + -8x + x2 = -17 Factor a perfect square on the left side: (x + -4)(x + -4) = -17 Can't calculate square root of the right side. The solution to this equation could not be determined.
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