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Simplifying 2w(w + 7 + -6 * 2 + 3 + -7 * 2 + 9) = -52 Multiply -6 * 2 2w(w + 7 + -12 + 3 + -7 * 2 + 9) = -52 Multiply -7 * 2 2w(w + 7 + -12 + 3 + -14 + 9) = -52 Reorder the terms: 2w(7 + -12 + 3 + -14 + 9 + w) = -52 Combine like terms: 7 + -12 = -5 2w(-5 + 3 + -14 + 9 + w) = -52 Combine like terms: -5 + 3 = -2 2w(-2 + -14 + 9 + w) = -52 Combine like terms: -2 + -14 = -16 2w(-16 + 9 + w) = -52 Combine like terms: -16 + 9 = -7 2w(-7 + w) = -52 (-7 * 2w + w * 2w) = -52 (-14w + 2w2) = -52 Solving -14w + 2w2 = -52 Solving for variable 'w'. Reorder the terms: 52 + -14w + 2w2 = -52 + 52 Combine like terms: -52 + 52 = 0 52 + -14w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(26 + -7w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + -7w + w2)' equal to zero and attempt to solve: Simplifying 26 + -7w + w2 = 0 Solving 26 + -7w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -7w + -26 + w2 = 0 + -26 Reorder the terms: 26 + -26 + -7w + w2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -7w + w2 = 0 + -26 -7w + w2 = 0 + -26 Combine like terms: 0 + -26 = -26 -7w + w2 = -26 The w term is -7w. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7w + 12.25 + w2 = -26 + 12.25 Reorder the terms: 12.25 + -7w + w2 = -26 + 12.25 Combine like terms: -26 + 12.25 = -13.75 12.25 + -7w + w2 = -13.75 Factor a perfect square on the left side: (w + -3.5)(w + -3.5) = -13.75 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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