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Simplifying 4x2 + 46x + 140 = 0 Reorder the terms: 140 + 46x + 4x2 = 0 Solving 140 + 46x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(70 + 23x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(70 + 23x + 2x2)' equal to zero and attempt to solve: Simplifying 70 + 23x + 2x2 = 0 Solving 70 + 23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 35 + 11.5x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + 11.5x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 11.5x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 11.5x + x2 = 0 + -35 11.5x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 11.5x + x2 = -35 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = -35 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = -35 + 33.0625 Combine like terms: -35 + 33.0625 = -1.9375 33.0625 + 11.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = -1.9375 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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