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Simplifying 16x2 + 512x + 11264 = 0 Reorder the terms: 11264 + 512x + 16x2 = 0 Solving 11264 + 512x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(704 + 32x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(704 + 32x + x2)' equal to zero and attempt to solve: Simplifying 704 + 32x + x2 = 0 Solving 704 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-704' to each side of the equation. 704 + 32x + -704 + x2 = 0 + -704 Reorder the terms: 704 + -704 + 32x + x2 = 0 + -704 Combine like terms: 704 + -704 = 0 0 + 32x + x2 = 0 + -704 32x + x2 = 0 + -704 Combine like terms: 0 + -704 = -704 32x + x2 = -704 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -704 + 256 Reorder the terms: 256 + 32x + x2 = -704 + 256 Combine like terms: -704 + 256 = -448 256 + 32x + x2 = -448 Factor a perfect square on the left side: (x + 16)(x + 16) = -448 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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