x^4-10x^2-75=0

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Solution for x^4-10x^2-75=0 equation:


Simplifying
x4 + -10x2 + -75 = 0

Reorder the terms:
-75 + -10x2 + x4 = 0

Solving
-75 + -10x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x2)(15 + -1x2) = 0

Subproblem 1

Set the factor '(-5 + -1x2)' equal to zero and attempt to solve: Simplifying -5 + -1x2 = 0 Solving -5 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x2 = 0 + 5 -1x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1x2 = 5 Divide each side by '-1'. x2 = -5 Simplifying x2 = -5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(15 + -1x2)' equal to zero and attempt to solve: Simplifying 15 + -1x2 = 0 Solving 15 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x2 = 0 + -15 -1x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -1x2 = -15 Divide each side by '-1'. x2 = 15 Simplifying x2 = 15 Take the square root of each side: x = {-3.872983346, 3.872983346}

Solution

x = {-3.872983346, 3.872983346}

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