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Simplifying 0 = x2 + 8x + 27 Reorder the terms: 0 = 27 + 8x + x2 Solving 0 = 27 + 8x + x2 Solving for variable 'x'. Combine like terms: 0 + -27 = -27 -27 + -8x + -1x2 = 27 + 8x + x2 + -27 + -8x + -1x2 Reorder the terms: -27 + -8x + -1x2 = 27 + -27 + 8x + -8x + x2 + -1x2 Combine like terms: 27 + -27 = 0 -27 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -27 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -27 + -8x + -1x2 = 0 + x2 + -1x2 -27 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -27 + -8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(27 + 8x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(27 + 8x + x2)' equal to zero and attempt to solve: Simplifying 27 + 8x + x2 = 0 Solving 27 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 8x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 8x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 8x + x2 = 0 + -27 8x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 8x + x2 = -27 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 = -27 + 16 Reorder the terms: 16 + 8x + x2 = -27 + 16 Combine like terms: -27 + 16 = -11 16 + 8x + x2 = -11 Factor a perfect square on the left side: (x + 4)(x + 4) = -11 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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