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Simplifying 4x2 + 32x + 208 = 0 Reorder the terms: 208 + 32x + 4x2 = 0 Solving 208 + 32x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(52 + 8x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(52 + 8x + x2)' equal to zero and attempt to solve: Simplifying 52 + 8x + x2 = 0 Solving 52 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + 8x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + 8x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + 8x + x2 = 0 + -52 8x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 8x + x2 = -52 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 = -52 + 16 Reorder the terms: 16 + 8x + x2 = -52 + 16 Combine like terms: -52 + 16 = -36 16 + 8x + x2 = -36 Factor a perfect square on the left side: (x + 4)(x + 4) = -36 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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