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Simplifying 3x2 + 27x + 135 = 0 Reorder the terms: 135 + 27x + 3x2 = 0 Solving 135 + 27x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(45 + 9x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(45 + 9x + x2)' equal to zero and attempt to solve: Simplifying 45 + 9x + x2 = 0 Solving 45 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 9x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 9x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 9x + x2 = 0 + -45 9x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 9x + x2 = -45 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -45 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -45 + 20.25 Combine like terms: -45 + 20.25 = -24.75 20.25 + 9x + x2 = -24.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = -24.75 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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