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Simplifying 6w = -15 + -3w2 Solving 6w = -15 + -3w2 Solving for variable 'w'. Reorder the terms: 15 + 6w + 3w2 = -15 + -3w2 + 15 + 3w2 Reorder the terms: 15 + 6w + 3w2 = -15 + 15 + -3w2 + 3w2 Combine like terms: -15 + 15 = 0 15 + 6w + 3w2 = 0 + -3w2 + 3w2 15 + 6w + 3w2 = -3w2 + 3w2 Combine like terms: -3w2 + 3w2 = 0 15 + 6w + 3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 2w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 2w + w2)' equal to zero and attempt to solve: Simplifying 5 + 2w + w2 = 0 Solving 5 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 2w + -5 + w2 = 0 + -5 Reorder the terms: 5 + -5 + 2w + w2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2w + w2 = 0 + -5 2w + w2 = 0 + -5 Combine like terms: 0 + -5 = -5 2w + w2 = -5 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = -5 + 1 Reorder the terms: 1 + 2w + w2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + 2w + w2 = -4 Factor a perfect square on the left side: (w + 1)(w + 1) = -4 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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