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Simplifying 14w4 + -23w2 + 8 = 0 Reorder the terms: 8 + -23w2 + 14w4 = 0 Solving 8 + -23w2 + 14w4 = 0 Solving for variable 'w'. Factor a trinomial. (1 + -2w2)(8 + -7w2) = 0Subproblem 1
Set the factor '(1 + -2w2)' equal to zero and attempt to solve: Simplifying 1 + -2w2 = 0 Solving 1 + -2w2 = 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 + -2w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w2 = 0 + -1 -2w2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2w2 = -1 Divide each side by '-2'. w2 = 0.5 Simplifying w2 = 0.5 Take the square root of each side: w = {-0.707106781, 0.707106781}Subproblem 2
Set the factor '(8 + -7w2)' equal to zero and attempt to solve: Simplifying 8 + -7w2 = 0 Solving 8 + -7w2 = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7w2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7w2 = 0 + -8 -7w2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7w2 = -8 Divide each side by '-7'. w2 = 1.142857143 Simplifying w2 = 1.142857143 Take the square root of each side: w = {-1.069044968, 1.069044968}Solution
w = {-0.707106781, 0.707106781, -1.069044968, 1.069044968}
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