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Simplifying w + -9w(w + 2) = 7 + -2w Reorder the terms: w + -9w(2 + w) = 7 + -2w w + (2 * -9w + w * -9w) = 7 + -2w w + (-18w + -9w2) = 7 + -2w Combine like terms: w + -18w = -17w -17w + -9w2 = 7 + -2w Solving -17w + -9w2 = 7 + -2w Solving for variable 'w'. Reorder the terms: -7 + -17w + 2w + -9w2 = 7 + -2w + -7 + 2w Combine like terms: -17w + 2w = -15w -7 + -15w + -9w2 = 7 + -2w + -7 + 2w Reorder the terms: -7 + -15w + -9w2 = 7 + -7 + -2w + 2w Combine like terms: 7 + -7 = 0 -7 + -15w + -9w2 = 0 + -2w + 2w -7 + -15w + -9w2 = -2w + 2w Combine like terms: -2w + 2w = 0 -7 + -15w + -9w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 15w + 9w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 15w + 9w2)' equal to zero and attempt to solve: Simplifying 7 + 15w + 9w2 = 0 Solving 7 + 15w + 9w2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + 1.666666667w + w2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 1.666666667w + -0.7777777778 + w2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 1.666666667w + w2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 1.666666667w + w2 = 0 + -0.7777777778 1.666666667w + w2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 1.666666667w + w2 = -0.7777777778 The w term is 1.666666667w. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667w + 0.6944444447 + w2 = -0.7777777778 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667w + w2 = -0.7777777778 + 0.6944444447 Combine like terms: -0.7777777778 + 0.6944444447 = -0.0833333331 0.6944444447 + 1.666666667w + w2 = -0.0833333331 Factor a perfect square on the left side: (w + 0.8333333335)(w + 0.8333333335) = -0.0833333331 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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