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Simplifying -1x2 + 16 + 8x = 24 + 12x Reorder the terms: 16 + 8x + -1x2 = 24 + 12x Solving 16 + 8x + -1x2 = 24 + 12x Solving for variable 'x'. Reorder the terms: 16 + -24 + 8x + -12x + -1x2 = 24 + 12x + -24 + -12x Combine like terms: 16 + -24 = -8 -8 + 8x + -12x + -1x2 = 24 + 12x + -24 + -12x Combine like terms: 8x + -12x = -4x -8 + -4x + -1x2 = 24 + 12x + -24 + -12x Reorder the terms: -8 + -4x + -1x2 = 24 + -24 + 12x + -12x Combine like terms: 24 + -24 = 0 -8 + -4x + -1x2 = 0 + 12x + -12x -8 + -4x + -1x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -8 + -4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 4x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 4x + x2)' equal to zero and attempt to solve: Simplifying 8 + 4x + x2 = 0 Solving 8 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 4x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 4x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 4x + x2 = 0 + -8 4x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 4x + x2 = -8 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -8 + 4 Reorder the terms: 4 + 4x + x2 = -8 + 4 Combine like terms: -8 + 4 = -4 4 + 4x + x2 = -4 Factor a perfect square on the left side: (x + 2)(x + 2) = -4 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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