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Simplifying (2w2 + -5 + -7) + -1(6w2 + 4w + -4) = 0 Reorder the terms: (-5 + -7 + 2w2) + -1(6w2 + 4w + -4) = 0 Combine like terms: -5 + -7 = -12 (-12 + 2w2) + -1(6w2 + 4w + -4) = 0 Remove parenthesis around (-12 + 2w2) -12 + 2w2 + -1(6w2 + 4w + -4) = 0 Reorder the terms: -12 + 2w2 + -1(-4 + 4w + 6w2) = 0 -12 + 2w2 + (-4 * -1 + 4w * -1 + 6w2 * -1) = 0 -12 + 2w2 + (4 + -4w + -6w2) = 0 Reorder the terms: -12 + 4 + -4w + 2w2 + -6w2 = 0 Combine like terms: -12 + 4 = -8 -8 + -4w + 2w2 + -6w2 = 0 Combine like terms: 2w2 + -6w2 = -4w2 -8 + -4w + -4w2 = 0 Solving -8 + -4w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-4'. -4(2 + w + w2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(2 + w + w2)' equal to zero and attempt to solve: Simplifying 2 + w + w2 = 0 Solving 2 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w + w2 = 0 + -2 w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 w + w2 = -2 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = -2 + 0.25 Reorder the terms: 0.25 + w + w2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + w + w2 = -1.75 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -1.75 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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