6x^4-23x^2=-7

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Solution for 6x^4-23x^2=-7 equation:


Simplifying
6x4 + -23x2 = -7

Reorder the terms:
-23x2 + 6x4 = -7

Solving
-23x2 + 6x4 = -7

Solving for variable 'x'.

Reorder the terms:
7 + -23x2 + 6x4 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + -23x2 + 6x4 = 0

Factor a trinomial.
(1 + -3x2)(7 + -2x2) = 0

Subproblem 1

Set the factor '(1 + -3x2)' equal to zero and attempt to solve: Simplifying 1 + -3x2 = 0 Solving 1 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x2 = 0 + -1 -3x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3x2 = -1 Divide each side by '-3'. x2 = 0.3333333333 Simplifying x2 = 0.3333333333 Take the square root of each side: x = {-0.577350269, 0.577350269}

Subproblem 2

Set the factor '(7 + -2x2)' equal to zero and attempt to solve: Simplifying 7 + -2x2 = 0 Solving 7 + -2x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x2 = 0 + -7 -2x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -2x2 = -7 Divide each side by '-2'. x2 = 3.5 Simplifying x2 = 3.5 Take the square root of each side: x = {-1.870828693, 1.870828693}

Solution

x = {-0.577350269, 0.577350269, -1.870828693, 1.870828693}

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