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Simplifying 4w4 + 40w2 = 44 Reorder the terms: 40w2 + 4w4 = 44 Solving 40w2 + 4w4 = 44 Solving for variable 'w'. Reorder the terms: -44 + 40w2 + 4w4 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 40w2 + 4w4 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + 10w2 + w4) = 0 Factor a trinomial. 4((-11 + -1w2)(1 + -1w2)) = 0 Factor a difference between two squares. 4((-11 + -1w2)((1 + w)(1 + -1w))) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + -1w2)' equal to zero and attempt to solve: Simplifying -11 + -1w2 = 0 Solving -11 + -1w2 = 0 Move all terms containing w to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1w2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1w2 = 0 + 11 -1w2 = 0 + 11 Combine like terms: 0 + 11 = 11 -1w2 = 11 Divide each side by '-1'. w2 = -11 Simplifying w2 = -11 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Subproblem 3
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {-1, 1}
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