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Simplifying 4x2 + 18x + 32 = 0 Reorder the terms: 32 + 18x + 4x2 = 0 Solving 32 + 18x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying 16 + 9x + 2x2 = 0 Solving 16 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8 + 4.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 4.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 4.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 4.5x + x2 = 0 + -8 4.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 4.5x + x2 = -8 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -8 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -8 + 5.0625 Combine like terms: -8 + 5.0625 = -2.9375 5.0625 + 4.5x + x2 = -2.9375 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -2.9375 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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