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Simplifying 4x2 + -28x + 54 = 0 Reorder the terms: 54 + -28x + 4x2 = 0 Solving 54 + -28x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -14x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying 27 + -14x + 2x2 = 0 Solving 27 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + -7x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -7x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -7x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -7x + x2 = 0 + -13.5 -7x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -7x + x2 = -13.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -13.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -13.5 + 12.25 Combine like terms: -13.5 + 12.25 = -1.25 12.25 + -7x + x2 = -1.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -1.25 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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