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Simplifying (7w2 + -2w + 16) + -4(7w2 + 15) = 0 Reorder the terms: (16 + -2w + 7w2) + -4(7w2 + 15) = 0 Remove parenthesis around (16 + -2w + 7w2) 16 + -2w + 7w2 + -4(7w2 + 15) = 0 Reorder the terms: 16 + -2w + 7w2 + -4(15 + 7w2) = 0 16 + -2w + 7w2 + (15 * -4 + 7w2 * -4) = 0 16 + -2w + 7w2 + (-60 + -28w2) = 0 Reorder the terms: 16 + -60 + -2w + 7w2 + -28w2 = 0 Combine like terms: 16 + -60 = -44 -44 + -2w + 7w2 + -28w2 = 0 Combine like terms: 7w2 + -28w2 = -21w2 -44 + -2w + -21w2 = 0 Solving -44 + -2w + -21w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(44 + 2w + 21w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(44 + 2w + 21w2)' equal to zero and attempt to solve: Simplifying 44 + 2w + 21w2 = 0 Solving 44 + 2w + 21w2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 2.095238095 + 0.09523809524w + w2 = 0 Move the constant term to the right: Add '-2.095238095' to each side of the equation. 2.095238095 + 0.09523809524w + -2.095238095 + w2 = 0 + -2.095238095 Reorder the terms: 2.095238095 + -2.095238095 + 0.09523809524w + w2 = 0 + -2.095238095 Combine like terms: 2.095238095 + -2.095238095 = 0.000000000 0.000000000 + 0.09523809524w + w2 = 0 + -2.095238095 0.09523809524w + w2 = 0 + -2.095238095 Combine like terms: 0 + -2.095238095 = -2.095238095 0.09523809524w + w2 = -2.095238095 The w term is 0.09523809524w. Take half its coefficient (0.04761904762). Square it (0.002267573696) and add it to both sides. Add '0.002267573696' to each side of the equation. 0.09523809524w + 0.002267573696 + w2 = -2.095238095 + 0.002267573696 Reorder the terms: 0.002267573696 + 0.09523809524w + w2 = -2.095238095 + 0.002267573696 Combine like terms: -2.095238095 + 0.002267573696 = -2.092970521304 0.002267573696 + 0.09523809524w + w2 = -2.092970521304 Factor a perfect square on the left side: (w + 0.04761904762)(w + 0.04761904762) = -2.092970521304 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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