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Simplifying -9w2 + 21w + -18 = 0 Reorder the terms: -18 + 21w + -9w2 = 0 Solving -18 + 21w + -9w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 7w + -3w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + 7w + -3w2)' equal to zero and attempt to solve: Simplifying -6 + 7w + -3w2 = 0 Solving -6 + 7w + -3w2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2 + -2.333333333w + w2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.333333333w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + -2.333333333w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.333333333w + w2 = 0 + -2 -2.333333333w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.333333333w + w2 = -2 The w term is -2.333333333w. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333w + 1.361111112 + w2 = -2 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333w + w2 = -2 + 1.361111112 Combine like terms: -2 + 1.361111112 = -0.638888888 1.361111112 + -2.333333333w + w2 = -0.638888888 Factor a perfect square on the left side: (w + -1.166666667)(w + -1.166666667) = -0.638888888 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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