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Simplifying 4x2 + -22x + 46 = 0 Reorder the terms: 46 + -22x + 4x2 = 0 Solving 46 + -22x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(23 + -11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + -11x + 2x2)' equal to zero and attempt to solve: Simplifying 23 + -11x + 2x2 = 0 Solving 23 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -5.5x + -11.5 + x2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + -5.5x + x2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -5.5x + x2 = 0 + -11.5 -5.5x + x2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 -5.5x + x2 = -11.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -11.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -11.5 + 7.5625 Combine like terms: -11.5 + 7.5625 = -3.9375 7.5625 + -5.5x + x2 = -3.9375 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = -3.9375 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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