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Simplifying 3x + -17 = x2 + 8x + 16 Reorder the terms: -17 + 3x = x2 + 8x + 16 Reorder the terms: -17 + 3x = 16 + 8x + x2 Solving -17 + 3x = 16 + 8x + x2 Solving for variable 'x'. Reorder the terms: -17 + -16 + 3x + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: -17 + -16 = -33 -33 + 3x + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 3x + -8x = -5x -33 + -5x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Reorder the terms: -33 + -5x + -1x2 = 16 + -16 + 8x + -8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 -33 + -5x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -33 + -5x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -33 + -5x + -1x2 = 0 + x2 + -1x2 -33 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -33 + -5x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(33 + 5x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(33 + 5x + x2)' equal to zero and attempt to solve: Simplifying 33 + 5x + x2 = 0 Solving 33 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 5x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + 5x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 5x + x2 = 0 + -33 5x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 5x + x2 = -33 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -33 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -33 + 6.25 Combine like terms: -33 + 6.25 = -26.75 6.25 + 5x + x2 = -26.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -26.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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