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Simplifying 40a4 + -200a2 + 250 = 0 Reorder the terms: 250 + -200a2 + 40a4 = 0 Solving 250 + -200a2 + 40a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '10'. 10(25 + -20a2 + 4a4) = 0 Factor a trinomial. 10((5 + -2a2)(5 + -2a2)) = 0 Ignore the factor 10.Subproblem 1
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}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 = {-1.58113883, 1.58113883, -1.58113883, 1.58113883}
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