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Simplifying 0 = 8x2 + 64x + 256 Reorder the terms: 0 = 256 + 64x + 8x2 Solving 0 = 256 + 64x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -256 = -256 -256 + -64x + -8x2 = 256 + 64x + 8x2 + -256 + -64x + -8x2 Reorder the terms: -256 + -64x + -8x2 = 256 + -256 + 64x + -64x + 8x2 + -8x2 Combine like terms: 256 + -256 = 0 -256 + -64x + -8x2 = 0 + 64x + -64x + 8x2 + -8x2 -256 + -64x + -8x2 = 64x + -64x + 8x2 + -8x2 Combine like terms: 64x + -64x = 0 -256 + -64x + -8x2 = 0 + 8x2 + -8x2 -256 + -64x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -256 + -64x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-8'. -8(32 + 8x + x2) = 0 Ignore the factor -8.Subproblem 1
Set the factor '(32 + 8x + x2)' equal to zero and attempt to solve: Simplifying 32 + 8x + x2 = 0 Solving 32 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 8x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 8x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 8x + x2 = 0 + -32 8x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 8x + x2 = -32 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 = -32 + 16 Reorder the terms: 16 + 8x + x2 = -32 + 16 Combine like terms: -32 + 16 = -16 16 + 8x + x2 = -16 Factor a perfect square on the left side: (x + 4)(x + 4) = -16 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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