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Simplifying 4x2 + -54x + 388 = 0 Reorder the terms: 388 + -54x + 4x2 = 0 Solving 388 + -54x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(194 + -27x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(194 + -27x + 2x2)' equal to zero and attempt to solve: Simplifying 194 + -27x + 2x2 = 0 Solving 194 + -27x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 97 + -13.5x + x2 = 0 Move the constant term to the right: Add '-97' to each side of the equation. 97 + -13.5x + -97 + x2 = 0 + -97 Reorder the terms: 97 + -97 + -13.5x + x2 = 0 + -97 Combine like terms: 97 + -97 = 0 0 + -13.5x + x2 = 0 + -97 -13.5x + x2 = 0 + -97 Combine like terms: 0 + -97 = -97 -13.5x + x2 = -97 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -97 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -97 + 45.5625 Combine like terms: -97 + 45.5625 = -51.4375 45.5625 + -13.5x + x2 = -51.4375 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = -51.4375 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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