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Simplifying (2w2 + -4w + -8) + -1(5w2 + 3w + -2) = 0 Reorder the terms: (-8 + -4w + 2w2) + -1(5w2 + 3w + -2) = 0 Remove parenthesis around (-8 + -4w + 2w2) -8 + -4w + 2w2 + -1(5w2 + 3w + -2) = 0 Reorder the terms: -8 + -4w + 2w2 + -1(-2 + 3w + 5w2) = 0 -8 + -4w + 2w2 + (-2 * -1 + 3w * -1 + 5w2 * -1) = 0 -8 + -4w + 2w2 + (2 + -3w + -5w2) = 0 Reorder the terms: -8 + 2 + -4w + -3w + 2w2 + -5w2 = 0 Combine like terms: -8 + 2 = -6 -6 + -4w + -3w + 2w2 + -5w2 = 0 Combine like terms: -4w + -3w = -7w -6 + -7w + 2w2 + -5w2 = 0 Combine like terms: 2w2 + -5w2 = -3w2 -6 + -7w + -3w2 = 0 Solving -6 + -7w + -3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 7w + 3w2) = 0 Ignore the factor -1.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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