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Simplifying 28w2 + 40w + 24 = 0 Reorder the terms: 24 + 40w + 28w2 = 0 Solving 24 + 40w + 28w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + 10w + 7w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + 10w + 7w2)' equal to zero and attempt to solve: Simplifying 6 + 10w + 7w2 = 0 Solving 6 + 10w + 7w2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 1.428571429w + w2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 1.428571429w + -0.8571428571 + w2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 1.428571429w + w2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 1.428571429w + w2 = 0 + -0.8571428571 1.428571429w + w2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 1.428571429w + w2 = -0.8571428571 The w term is 1.428571429w. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429w + 0.5102040819 + w2 = -0.8571428571 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429w + w2 = -0.8571428571 + 0.5102040819 Combine like terms: -0.8571428571 + 0.5102040819 = -0.3469387752 0.5102040819 + 1.428571429w + w2 = -0.3469387752 Factor a perfect square on the left side: (w + 0.7142857145)(w + 0.7142857145) = -0.3469387752 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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