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Simplifying 2x2 + -20x + 54 = 0 Reorder the terms: 54 + -20x + 2x2 = 0 Solving 54 + -20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -10x + x2)' equal to zero and attempt to solve: Simplifying 27 + -10x + x2 = 0 Solving 27 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -10x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -10x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -10x + x2 = 0 + -27 -10x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -10x + x2 = -27 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -27 + 25 Reorder the terms: 25 + -10x + x2 = -27 + 25 Combine like terms: -27 + 25 = -2 25 + -10x + x2 = -2 Factor a perfect square on the left side: (x + -5)(x + -5) = -2 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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