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Simplifying (-5w2 + -7w + -9) + -1(-4w2 + 6w + 5) + (-6w2 + -3w + 2) = 0 Reorder the terms: (-9 + -7w + -5w2) + -1(-4w2 + 6w + 5) + (-6w2 + -3w + 2) = 0 Remove parenthesis around (-9 + -7w + -5w2) -9 + -7w + -5w2 + -1(-4w2 + 6w + 5) + (-6w2 + -3w + 2) = 0 Reorder the terms: -9 + -7w + -5w2 + -1(5 + 6w + -4w2) + (-6w2 + -3w + 2) = 0 -9 + -7w + -5w2 + (5 * -1 + 6w * -1 + -4w2 * -1) + (-6w2 + -3w + 2) = 0 -9 + -7w + -5w2 + (-5 + -6w + 4w2) + (-6w2 + -3w + 2) = 0 Reorder the terms: -9 + -7w + -5w2 + -5 + -6w + 4w2 + (2 + -3w + -6w2) = 0 Remove parenthesis around (2 + -3w + -6w2) -9 + -7w + -5w2 + -5 + -6w + 4w2 + 2 + -3w + -6w2 = 0 Reorder the terms: -9 + -5 + 2 + -7w + -6w + -3w + -5w2 + 4w2 + -6w2 = 0 Combine like terms: -9 + -5 = -14 -14 + 2 + -7w + -6w + -3w + -5w2 + 4w2 + -6w2 = 0 Combine like terms: -14 + 2 = -12 -12 + -7w + -6w + -3w + -5w2 + 4w2 + -6w2 = 0 Combine like terms: -7w + -6w = -13w -12 + -13w + -3w + -5w2 + 4w2 + -6w2 = 0 Combine like terms: -13w + -3w = -16w -12 + -16w + -5w2 + 4w2 + -6w2 = 0 Combine like terms: -5w2 + 4w2 = -1w2 -12 + -16w + -1w2 + -6w2 = 0 Combine like terms: -1w2 + -6w2 = -7w2 -12 + -16w + -7w2 = 0 Solving -12 + -16w + -7w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 16w + 7w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 16w + 7w2)' equal to zero and attempt to solve: Simplifying 12 + 16w + 7w2 = 0 Solving 12 + 16w + 7w2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.714285714 + 2.285714286w + w2 = 0 Move the constant term to the right: Add '-1.714285714' to each side of the equation. 1.714285714 + 2.285714286w + -1.714285714 + w2 = 0 + -1.714285714 Reorder the terms: 1.714285714 + -1.714285714 + 2.285714286w + w2 = 0 + -1.714285714 Combine like terms: 1.714285714 + -1.714285714 = 0.000000000 0.000000000 + 2.285714286w + w2 = 0 + -1.714285714 2.285714286w + w2 = 0 + -1.714285714 Combine like terms: 0 + -1.714285714 = -1.714285714 2.285714286w + w2 = -1.714285714 The w term is 2.285714286w. Take half its coefficient (1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. 2.285714286w + 1.306122449 + w2 = -1.714285714 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286w + w2 = -1.714285714 + 1.306122449 Combine like terms: -1.714285714 + 1.306122449 = -0.408163265 1.306122449 + 2.285714286w + w2 = -0.408163265 Factor a perfect square on the left side: (w + 1.142857143)(w + 1.142857143) = -0.408163265 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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