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Simplifying 6(8a4 + -42a2 + 49) = 0 Reorder the terms: 6(49 + -42a2 + 8a4) = 0 (49 * 6 + -42a2 * 6 + 8a4 * 6) = 0 (294 + -252a2 + 48a4) = 0 Solving 294 + -252a2 + 48a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(49 + -42a2 + 8a4) = 0 Factor a trinomial. 6((7 + -4a2)(7 + -2a2)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + -4a2)' equal to zero and attempt to solve: Simplifying 7 + -4a2 = 0 Solving 7 + -4a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4a2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a2 = 0 + -7 -4a2 = 0 + -7 Combine like terms: 0 + -7 = -7 -4a2 = -7 Divide each side by '-4'. a2 = 1.75 Simplifying a2 = 1.75 Take the square root of each side: a = {-1.322875656, 1.322875656}Subproblem 2
Set the factor '(7 + -2a2)' equal to zero and attempt to solve: Simplifying 7 + -2a2 = 0 Solving 7 + -2a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2a2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2a2 = 0 + -7 -2a2 = 0 + -7 Combine like terms: 0 + -7 = -7 -2a2 = -7 Divide each side by '-2'. a2 = 3.5 Simplifying a2 = 3.5 Take the square root of each side: a = {-1.870828693, 1.870828693}Solution
a = {-1.322875656, 1.322875656, -1.870828693, 1.870828693}
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