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Simplifying 72w4 + -32w2 = 0 Reorder the terms: -32w2 + 72w4 = 0 Solving -32w2 + 72w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '8w2'. 8w2(-4 + 9w2) = 0 Factor a difference between two squares. 8w2((2 + 3w)(-2 + 3w)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve: Simplifying w2 = 0 Solving w2 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w2 = 0 Take the square root of each side: w = {0}Subproblem 2
Set the factor '(2 + 3w)' equal to zero and attempt to solve: Simplifying 2 + 3w = 0 Solving 2 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3w = 0 + -2 3w = 0 + -2 Combine like terms: 0 + -2 = -2 3w = -2 Divide each side by '3'. w = -0.6666666667 Simplifying w = -0.6666666667Subproblem 3
Set the factor '(-2 + 3w)' equal to zero and attempt to solve: Simplifying -2 + 3w = 0 Solving -2 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3w = 0 + 2 3w = 0 + 2 Combine like terms: 0 + 2 = 2 3w = 2 Divide each side by '3'. w = 0.6666666667 Simplifying w = 0.6666666667Solution
w = {0, -0.6666666667, 0.6666666667}
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