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Simplifying (4w2 + -5w + -7) + -1(8w2 + 3w + -2) = 0 Reorder the terms: (-7 + -5w + 4w2) + -1(8w2 + 3w + -2) = 0 Remove parenthesis around (-7 + -5w + 4w2) -7 + -5w + 4w2 + -1(8w2 + 3w + -2) = 0 Reorder the terms: -7 + -5w + 4w2 + -1(-2 + 3w + 8w2) = 0 -7 + -5w + 4w2 + (-2 * -1 + 3w * -1 + 8w2 * -1) = 0 -7 + -5w + 4w2 + (2 + -3w + -8w2) = 0 Reorder the terms: -7 + 2 + -5w + -3w + 4w2 + -8w2 = 0 Combine like terms: -7 + 2 = -5 -5 + -5w + -3w + 4w2 + -8w2 = 0 Combine like terms: -5w + -3w = -8w -5 + -8w + 4w2 + -8w2 = 0 Combine like terms: 4w2 + -8w2 = -4w2 -5 + -8w + -4w2 = 0 Solving -5 + -8w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 8w + 4w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 8w + 4w2)' equal to zero and attempt to solve: Simplifying 5 + 8w + 4w2 = 0 Solving 5 + 8w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 2w + w2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 2w + -1.25 + w2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 2w + w2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 2w + w2 = 0 + -1.25 2w + w2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 2w + w2 = -1.25 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = -1.25 + 1 Reorder the terms: 1 + 2w + w2 = -1.25 + 1 Combine like terms: -1.25 + 1 = -0.25 1 + 2w + w2 = -0.25 Factor a perfect square on the left side: (w + 1)(w + 1) = -0.25 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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