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Simplifying Y4 + -10Y2 + 21 = 0 Reorder the terms: 21 + -10Y2 + Y4 = 0 Solving 21 + -10Y2 + Y4 = 0 Solving for variable 'Y'. Factor a trinomial. (3 + -1Y2)(7 + -1Y2) = 0Subproblem 1
Set the factor '(3 + -1Y2)' equal to zero and attempt to solve: Simplifying 3 + -1Y2 = 0 Solving 3 + -1Y2 = 0 Move all terms containing Y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1Y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1Y2 = 0 + -3 -1Y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1Y2 = -3 Divide each side by '-1'. Y2 = 3 Simplifying Y2 = 3 Take the square root of each side: Y = {-1.732050808, 1.732050808}Subproblem 2
Set the factor '(7 + -1Y2)' equal to zero and attempt to solve: Simplifying 7 + -1Y2 = 0 Solving 7 + -1Y2 = 0 Move all terms containing Y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1Y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1Y2 = 0 + -7 -1Y2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1Y2 = -7 Divide each side by '-1'. Y2 = 7 Simplifying Y2 = 7 Take the square root of each side: Y = {-2.645751311, 2.645751311}Solution
Y = {-1.732050808, 1.732050808, -2.645751311, 2.645751311}
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