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Simplifying 8x2 + 36x + 162 = 0 Reorder the terms: 162 + 36x + 8x2 = 0 Solving 162 + 36x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(81 + 18x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(81 + 18x + 4x2)' equal to zero and attempt to solve: Simplifying 81 + 18x + 4x2 = 0 Solving 81 + 18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 20.25 + 4.5x + x2 = 0 Move the constant term to the right: Add '-20.25' to each side of the equation. 20.25 + 4.5x + -20.25 + x2 = 0 + -20.25 Reorder the terms: 20.25 + -20.25 + 4.5x + x2 = 0 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + 4.5x + x2 = 0 + -20.25 4.5x + x2 = 0 + -20.25 Combine like terms: 0 + -20.25 = -20.25 4.5x + x2 = -20.25 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 = -20.25 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -20.25 + 5.0625 Combine like terms: -20.25 + 5.0625 = -15.1875 5.0625 + 4.5x + x2 = -15.1875 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -15.1875 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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