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Simplifying 16x2 + 128x + 4096 = 0 Reorder the terms: 4096 + 128x + 16x2 = 0 Solving 4096 + 128x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(256 + 8x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(256 + 8x + x2)' equal to zero and attempt to solve: Simplifying 256 + 8x + x2 = 0 Solving 256 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + 8x + -256 + x2 = 0 + -256 Reorder the terms: 256 + -256 + 8x + x2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + 8x + x2 = 0 + -256 8x + x2 = 0 + -256 Combine like terms: 0 + -256 = -256 8x + x2 = -256 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 = -256 + 16 Reorder the terms: 16 + 8x + x2 = -256 + 16 Combine like terms: -256 + 16 = -240 16 + 8x + x2 = -240 Factor a perfect square on the left side: (x + 4)(x + 4) = -240 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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