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Simplifying 6x2 + 18x + 54 = 0 Reorder the terms: 54 + 18x + 6x2 = 0 Solving 54 + 18x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(9 + 3x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(9 + 3x + x2)' equal to zero and attempt to solve: Simplifying 9 + 3x + x2 = 0 Solving 9 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 3x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 3x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 3x + x2 = 0 + -9 3x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 3x + x2 = -9 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -9 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -9 + 2.25 Combine like terms: -9 + 2.25 = -6.75 2.25 + 3x + x2 = -6.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -6.75 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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