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Simplifying 4x2 + -22x + 112 = 0 Reorder the terms: 112 + -22x + 4x2 = 0 Solving 112 + -22x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(56 + -11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(56 + -11x + 2x2)' equal to zero and attempt to solve: Simplifying 56 + -11x + 2x2 = 0 Solving 56 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 28 + -5.5x + x2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -5.5x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -5.5x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -5.5x + x2 = 0 + -28 -5.5x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -5.5x + x2 = -28 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 = -28 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -28 + 7.5625 Combine like terms: -28 + 7.5625 = -20.4375 7.5625 + -5.5x + x2 = -20.4375 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = -20.4375 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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