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Simplifying 4a4 + -12a2 + 5 = 0 Reorder the terms: 5 + -12a2 + 4a4 = 0 Solving 5 + -12a2 + 4a4 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -2a2)(5 + -2a2) = 0Subproblem 1
Set the factor '(1 + -2a2)' equal to zero and attempt to solve: Simplifying 1 + -2a2 = 0 Solving 1 + -2a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a2 = 0 + -1 -2a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2a2 = -1 Divide each side by '-2'. a2 = 0.5 Simplifying a2 = 0.5 Take the square root of each side: a = {-0.707106781, 0.707106781}Subproblem 2
Set the factor '(5 + -2a2)' equal to zero and attempt to solve: Simplifying 5 + -2a2 = 0 Solving 5 + -2a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a2 = 0 + -5 -2a2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2a2 = -5 Divide each side by '-2'. a2 = 2.5 Simplifying a2 = 2.5 Take the square root of each side: a = {-1.58113883, 1.58113883}Solution
a = {-0.707106781, 0.707106781, -1.58113883, 1.58113883}
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