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Simplifying a * a = (a * a * a * a) + -1(0.5 * 4) Multiply a * a a2 = (a * a * a * a) + -1(0.5 * 4) Multiply a * a a2 = (a2 * a * a) + -1(0.5 * 4) Multiply a2 * a a2 = (a3 * a) + -1(0.5 * 4) Multiply a3 * a a2 = (a4) + -1(0.5 * 4) a2 = a4 + -1(0.5 * 4) Multiply 0.5 * 4 a2 = a4 + -1(2) Multiply -1 * 2 a2 = a4 + -2 Reorder the terms: a2 = -2 + a4 Solving a2 = -2 + a4 Solving for variable 'a'. Reorder the terms: 2 + a2 + -1a4 = -2 + a4 + 2 + -1a4 Reorder the terms: 2 + a2 + -1a4 = -2 + 2 + a4 + -1a4 Combine like terms: -2 + 2 = 0 2 + a2 + -1a4 = 0 + a4 + -1a4 2 + a2 + -1a4 = a4 + -1a4 Combine like terms: a4 + -1a4 = 0 2 + a2 + -1a4 = 0 Factor a trinomial. (2 + -1a2)(1 + a2) = 0Subproblem 1
Set the factor '(2 + -1a2)' equal to zero and attempt to solve: Simplifying 2 + -1a2 = 0 Solving 2 + -1a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a2 = 0 + -2 -1a2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1a2 = -2 Divide each side by '-1'. a2 = 2 Simplifying a2 = 2 Take the square root of each side: a = {-1.414213562, 1.414213562}Subproblem 2
Set the factor '(1 + a2)' equal to zero and attempt to solve: Simplifying 1 + a2 = 0 Solving 1 + a2 = 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 + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a2 = 0 + -1 a2 = 0 + -1 Combine like terms: 0 + -1 = -1 a2 = -1 Simplifying a2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {-1.414213562, 1.414213562}
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