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Simplifying -210 = w2 + 3w Reorder the terms: -210 = 3w + w2 Solving -210 = 3w + w2 Solving for variable 'w'. Reorder the terms: -210 + -3w + -1w2 = 3w + -3w + w2 + -1w2 Combine like terms: 3w + -3w = 0 -210 + -3w + -1w2 = 0 + w2 + -1w2 -210 + -3w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -210 + -3w + -1w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(210 + 3w + w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(210 + 3w + w2)' equal to zero and attempt to solve: Simplifying 210 + 3w + w2 = 0 Solving 210 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-210' to each side of the equation. 210 + 3w + -210 + w2 = 0 + -210 Reorder the terms: 210 + -210 + 3w + w2 = 0 + -210 Combine like terms: 210 + -210 = 0 0 + 3w + w2 = 0 + -210 3w + w2 = 0 + -210 Combine like terms: 0 + -210 = -210 3w + w2 = -210 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = -210 + 2.25 Reorder the terms: 2.25 + 3w + w2 = -210 + 2.25 Combine like terms: -210 + 2.25 = -207.75 2.25 + 3w + w2 = -207.75 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = -207.75 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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