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Simplifying (6w + -11w2) + -1(4 + 7w2) = 0 Remove parenthesis around (6w + -11w2) 6w + -11w2 + -1(4 + 7w2) = 0 6w + -11w2 + (4 * -1 + 7w2 * -1) = 0 6w + -11w2 + (-4 + -7w2) = 0 Reorder the terms: -4 + 6w + -11w2 + -7w2 = 0 Combine like terms: -11w2 + -7w2 = -18w2 -4 + 6w + -18w2 = 0 Solving -4 + 6w + -18w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 3w + -9w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 3w + -9w2)' equal to zero and attempt to solve: Simplifying -2 + 3w + -9w2 = 0 Solving -2 + 3w + -9w2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.2222222222 + -0.3333333333w + w2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.3333333333w + -0.2222222222 + w2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -0.3333333333w + w2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -0.3333333333w + w2 = 0 + -0.2222222222 -0.3333333333w + w2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -0.3333333333w + w2 = -0.2222222222 The w term is -0.3333333333w. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333w + 0.02777777779 + w2 = -0.2222222222 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333w + w2 = -0.2222222222 + 0.02777777779 Combine like terms: -0.2222222222 + 0.02777777779 = -0.19444444441 0.02777777779 + -0.3333333333w + w2 = -0.19444444441 Factor a perfect square on the left side: (w + -0.1666666667)(w + -0.1666666667) = -0.19444444441 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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