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Simplifying (6(w2)) + -1(144w) + 2 = 0 Remove parenthesis around (144w) (6w2) + -1 * 144w + 2 = 0 Multiply -1 * 144 (6w2) + -144w + 2 = 0 Reorder the terms: 2 + -144w + (6w2) = 0 Solving 2 + -144w + (6w2) = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -72w + (3w2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -72w + (3w2))' equal to zero and attempt to solve: Simplifying 1 + -72w + (3w2) = 0 Solving 1 + -72w + (3w2) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -24w + w2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -24w + -0.3333333333 + w2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -24w + w2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -24w + w2 = 0 + -0.3333333333 -24w + w2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -24w + w2 = -0.3333333333 The w term is -24w. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24w + 144 + w2 = -0.3333333333 + 144 Reorder the terms: 144 + -24w + w2 = -0.3333333333 + 144 Combine like terms: -0.3333333333 + 144 = 143.6666666667 144 + -24w + w2 = 143.6666666667 Factor a perfect square on the left side: ((w) + -12)((w) + -12) = 143.6666666667 Calculate the square root of the right side: 11.986103064 Break this problem into two subproblems by setting ((w) + -12) equal to 11.986103064 and -11.986103064.Subproblem 1
(w) + -12 = 11.986103064 Simplifying (w) + -12 = 11.986103064 w + -12 = 11.986103064 Reorder the terms: -12 + w = 11.986103064 Solving -12 + w = 11.986103064 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + w = 11.986103064 + 12 Combine like terms: -12 + 12 = 0 0 + w = 11.986103064 + 12 w = 11.986103064 + 12 Combine like terms: 11.986103064 + 12 = 23.986103064 w = 23.986103064 Simplifying w = 23.986103064Subproblem 2
(w) + -12 = -11.986103064 Simplifying (w) + -12 = -11.986103064 w + -12 = -11.986103064 Reorder the terms: -12 + w = -11.986103064 Solving -12 + w = -11.986103064 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + w = -11.986103064 + 12 Combine like terms: -12 + 12 = 0 0 + w = -11.986103064 + 12 w = -11.986103064 + 12 Combine like terms: -11.986103064 + 12 = 0.013896936 w = 0.013896936 Simplifying w = 0.013896936Solution
The solution to the problem is based on the solutions from the subproblems. w = {23.986103064, 0.013896936}Solution
w = {23.986103064, 0.013896936}
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