d^4-11d^2+24=0

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Solution for d^4-11d^2+24=0 equation:


Simplifying
d4 + -11d2 + 24 = 0

Reorder the terms:
24 + -11d2 + d4 = 0

Solving
24 + -11d2 + d4 = 0

Solving for variable 'd'.

Factor a trinomial.
(3 + -1d2)(8 + -1d2) = 0

Subproblem 1

Set the factor '(3 + -1d2)' equal to zero and attempt to solve: Simplifying 3 + -1d2 = 0 Solving 3 + -1d2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1d2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1d2 = 0 + -3 -1d2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1d2 = -3 Divide each side by '-1'. d2 = 3 Simplifying d2 = 3 Take the square root of each side: d = {-1.732050808, 1.732050808}

Subproblem 2

Set the factor '(8 + -1d2)' equal to zero and attempt to solve: Simplifying 8 + -1d2 = 0 Solving 8 + -1d2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1d2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1d2 = 0 + -8 -1d2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1d2 = -8 Divide each side by '-1'. d2 = 8 Simplifying d2 = 8 Take the square root of each side: d = {-2.828427125, 2.828427125}

Solution

d = {-1.732050808, 1.732050808, -2.828427125, 2.828427125}

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