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Simplifying 2w2 + 4w + 22 = 0 Reorder the terms: 22 + 4w + 2w2 = 0 Solving 22 + 4w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 2w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 2w + w2)' equal to zero and attempt to solve: Simplifying 11 + 2w + w2 = 0 Solving 11 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 2w + -11 + w2 = 0 + -11 Reorder the terms: 11 + -11 + 2w + w2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 2w + w2 = 0 + -11 2w + w2 = 0 + -11 Combine like terms: 0 + -11 = -11 2w + w2 = -11 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = -11 + 1 Reorder the terms: 1 + 2w + w2 = -11 + 1 Combine like terms: -11 + 1 = -10 1 + 2w + w2 = -10 Factor a perfect square on the left side: (w + 1)(w + 1) = -10 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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