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Simplifying -2w2 + -5w + -52 = 0 Reorder the terms: -52 + -5w + -2w2 = 0 Solving -52 + -5w + -2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(52 + 5w + 2w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(52 + 5w + 2w2)' equal to zero and attempt to solve: Simplifying 52 + 5w + 2w2 = 0 Solving 52 + 5w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 26 + 2.5w + w2 = 0 Move the constant term to the right: Add '-26' to each side of the equation. 26 + 2.5w + -26 + w2 = 0 + -26 Reorder the terms: 26 + -26 + 2.5w + w2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 2.5w + w2 = 0 + -26 2.5w + w2 = 0 + -26 Combine like terms: 0 + -26 = -26 2.5w + w2 = -26 The w term is 2.5w. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5w + 1.5625 + w2 = -26 + 1.5625 Reorder the terms: 1.5625 + 2.5w + w2 = -26 + 1.5625 Combine like terms: -26 + 1.5625 = -24.4375 1.5625 + 2.5w + w2 = -24.4375 Factor a perfect square on the left side: (w + 1.25)(w + 1.25) = -24.4375 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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