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Simplifying 90w2 + -90w + 25 = 0 Reorder the terms: 25 + -90w + 90w2 = 0 Solving 25 + -90w + 90w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -18w + 18w2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -18w + 18w2)' equal to zero and attempt to solve: Simplifying 5 + -18w + 18w2 = 0 Solving 5 + -18w + 18w2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2777777778 + -1w + w2 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + -1w + -0.2777777778 + w2 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + -1w + w2 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + -1w + w2 = 0 + -0.2777777778 -1w + w2 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 -1w + w2 = -0.2777777778 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 = -0.2777777778 + 0.25 Reorder the terms: 0.25 + -1w + w2 = -0.2777777778 + 0.25 Combine like terms: -0.2777777778 + 0.25 = -0.0277777778 0.25 + -1w + w2 = -0.0277777778 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = -0.0277777778 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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