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Simplifying -4w2 + -9w + -7 = 0 Reorder the terms: -7 + -9w + -4w2 = 0 Solving -7 + -9w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 9w + 4w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 9w + 4w2)' equal to zero and attempt to solve: Simplifying 7 + 9w + 4w2 = 0 Solving 7 + 9w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 2.25w + w2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 2.25w + -1.75 + w2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 2.25w + w2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 2.25w + w2 = 0 + -1.75 2.25w + w2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 2.25w + w2 = -1.75 The w term is 2.25w. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25w + 1.265625 + w2 = -1.75 + 1.265625 Reorder the terms: 1.265625 + 2.25w + w2 = -1.75 + 1.265625 Combine like terms: -1.75 + 1.265625 = -0.484375 1.265625 + 2.25w + w2 = -0.484375 Factor a perfect square on the left side: (w + 1.125)(w + 1.125) = -0.484375 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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