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Simplifying 4z4 + -12z2 + 5 = 0 Reorder the terms: 5 + -12z2 + 4z4 = 0 Solving 5 + -12z2 + 4z4 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -2z2)(5 + -2z2) = 0Subproblem 1
Set the factor '(1 + -2z2)' equal to zero and attempt to solve: Simplifying 1 + -2z2 = 0 Solving 1 + -2z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z2 = 0 + -1 -2z2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2z2 = -1 Divide each side by '-2'. z2 = 0.5 Simplifying z2 = 0.5 Take the square root of each side: z = {-0.707106781, 0.707106781}Subproblem 2
Set the factor '(5 + -2z2)' equal to zero and attempt to solve: Simplifying 5 + -2z2 = 0 Solving 5 + -2z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2z2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z2 = 0 + -5 -2z2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2z2 = -5 Divide each side by '-2'. z2 = 2.5 Simplifying z2 = 2.5 Take the square root of each side: z = {-1.58113883, 1.58113883}Solution
z = {-0.707106781, 0.707106781, -1.58113883, 1.58113883}
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