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Simplifying 5w2 = 5w + -10 Reorder the terms: 5w2 = -10 + 5w Solving 5w2 = -10 + 5w Solving for variable 'w'. Reorder the terms: 10 + -5w + 5w2 = -10 + 5w + 10 + -5w Reorder the terms: 10 + -5w + 5w2 = -10 + 10 + 5w + -5w Combine like terms: -10 + 10 = 0 10 + -5w + 5w2 = 0 + 5w + -5w 10 + -5w + 5w2 = 5w + -5w Combine like terms: 5w + -5w = 0 10 + -5w + 5w2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -1w + w2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -1w + w2)' equal to zero and attempt to solve: Simplifying 2 + -1w + w2 = 0 Solving 2 + -1w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + -1w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w + w2 = 0 + -2 -1w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1w + w2 = -2 The w term is -1w. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1w + 0.25 + w2 = -2 + 0.25 Reorder the terms: 0.25 + -1w + w2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + -1w + w2 = -1.75 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = -1.75 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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