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Simplifying 8x2 + 4x + 32 = 0 Reorder the terms: 32 + 4x + 8x2 = 0 Solving 32 + 4x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + x + 2x2)' equal to zero and attempt to solve: Simplifying 8 + x + 2x2 = 0 Solving 8 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 0.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 0.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 0.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 0.5x + x2 = 0 + -4 0.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 0.5x + x2 = -4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = -4 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + 0.5x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 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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