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Simplifying 90 = -2w2 + 8w Reorder the terms: 90 = 8w + -2w2 Solving 90 = 8w + -2w2 Solving for variable 'w'. Reorder the terms: 90 + -8w + 2w2 = 8w + -8w + -2w2 + 2w2 Combine like terms: 8w + -8w = 0 90 + -8w + 2w2 = 0 + -2w2 + 2w2 90 + -8w + 2w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 90 + -8w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -4w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -4w + w2)' equal to zero and attempt to solve: Simplifying 45 + -4w + w2 = 0 Solving 45 + -4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -4w + -45 + w2 = 0 + -45 Reorder the terms: 45 + -45 + -4w + w2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -4w + w2 = 0 + -45 -4w + w2 = 0 + -45 Combine like terms: 0 + -45 = -45 -4w + w2 = -45 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = -45 + 4 Reorder the terms: 4 + -4w + w2 = -45 + 4 Combine like terms: -45 + 4 = -41 4 + -4w + w2 = -41 Factor a perfect square on the left side: (w + -2)(w + -2) = -41 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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