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Simplifying 4w2 + -24w + 90 = 0 Reorder the terms: 90 + -24w + 4w2 = 0 Solving 90 + -24w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -12w + 2w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -12w + 2w2)' equal to zero and attempt to solve: Simplifying 45 + -12w + 2w2 = 0 Solving 45 + -12w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + -6w + w2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -6w + -22.5 + w2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -6w + w2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -6w + w2 = 0 + -22.5 -6w + w2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -6w + w2 = -22.5 The w term is -6w. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6w + 9 + w2 = -22.5 + 9 Reorder the terms: 9 + -6w + w2 = -22.5 + 9 Combine like terms: -22.5 + 9 = -13.5 9 + -6w + w2 = -13.5 Factor a perfect square on the left side: (w + -3)(w + -3) = -13.5 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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