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Simplifying 12w2 + -2w + 64 = 0 Reorder the terms: 64 + -2w + 12w2 = 0 Solving 64 + -2w + 12w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + -1w + 6w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + -1w + 6w2)' equal to zero and attempt to solve: Simplifying 32 + -1w + 6w2 = 0 Solving 32 + -1w + 6w2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 5.333333333 + -0.1666666667w + w2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -0.1666666667w + -5.333333333 + w2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -0.1666666667w + w2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -0.1666666667w + w2 = 0 + -5.333333333 -0.1666666667w + w2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -0.1666666667w + w2 = -5.333333333 The w term is -0.1666666667w. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667w + 0.006944444447 + w2 = -5.333333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667w + w2 = -5.333333333 + 0.006944444447 Combine like terms: -5.333333333 + 0.006944444447 = -5.326388888553 0.006944444447 + -0.1666666667w + w2 = -5.326388888553 Factor a perfect square on the left side: (w + -0.08333333335)(w + -0.08333333335) = -5.326388888553 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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