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Simplifying (7w2 + -5w + -2) + (3w2 + -1w + 6) = 0 Reorder the terms: (-2 + -5w + 7w2) + (3w2 + -1w + 6) = 0 Remove parenthesis around (-2 + -5w + 7w2) -2 + -5w + 7w2 + (3w2 + -1w + 6) = 0 Reorder the terms: -2 + -5w + 7w2 + (6 + -1w + 3w2) = 0 Remove parenthesis around (6 + -1w + 3w2) -2 + -5w + 7w2 + 6 + -1w + 3w2 = 0 Reorder the terms: -2 + 6 + -5w + -1w + 7w2 + 3w2 = 0 Combine like terms: -2 + 6 = 4 4 + -5w + -1w + 7w2 + 3w2 = 0 Combine like terms: -5w + -1w = -6w 4 + -6w + 7w2 + 3w2 = 0 Combine like terms: 7w2 + 3w2 = 10w2 4 + -6w + 10w2 = 0 Solving 4 + -6w + 10w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -3w + 5w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3w + 5w2)' equal to zero and attempt to solve: Simplifying 2 + -3w + 5w2 = 0 Solving 2 + -3w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -0.6w + w2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.6w + -0.4 + w2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.6w + w2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.6w + w2 = 0 + -0.4 -0.6w + w2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.6w + w2 = -0.4 The w term is -0.6w. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6w + 0.09 + w2 = -0.4 + 0.09 Reorder the terms: 0.09 + -0.6w + w2 = -0.4 + 0.09 Combine like terms: -0.4 + 0.09 = -0.31 0.09 + -0.6w + w2 = -0.31 Factor a perfect square on the left side: (w + -0.3)(w + -0.3) = -0.31 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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