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Simplifying 3x2 + 3x + 108 = 0 Reorder the terms: 108 + 3x + 3x2 = 0 Solving 108 + 3x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(36 + x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(36 + x + x2)' equal to zero and attempt to solve: Simplifying 36 + x + x2 = 0 Solving 36 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + x + x2 = 0 + -36 x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 x + x2 = -36 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. x + 0.25 + x2 = -36 + 0.25 Reorder the terms: 0.25 + x + x2 = -36 + 0.25 Combine like terms: -36 + 0.25 = -35.75 0.25 + x + x2 = -35.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -35.75 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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