5X^4-3X^2=7X^6-5X^4

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Solution for 5X^4-3X^2=7X^6-5X^4 equation:


Simplifying
5X4 + -3X2 = 7X6 + -5X4

Reorder the terms:
-3X2 + 5X4 = 7X6 + -5X4

Reorder the terms:
-3X2 + 5X4 = -5X4 + 7X6

Solving
-3X2 + 5X4 = -5X4 + 7X6

Solving for variable 'X'.

Combine like terms: 5X4 + 5X4 = 10X4
-3X2 + 10X4 + -7X6 = -5X4 + 7X6 + 5X4 + -7X6

Reorder the terms:
-3X2 + 10X4 + -7X6 = -5X4 + 5X4 + 7X6 + -7X6

Combine like terms: -5X4 + 5X4 = 0
-3X2 + 10X4 + -7X6 = 0 + 7X6 + -7X6
-3X2 + 10X4 + -7X6 = 7X6 + -7X6

Combine like terms: 7X6 + -7X6 = 0
-3X2 + 10X4 + -7X6 = 0

Factor out the Greatest Common Factor (GCF), 'X2'.
X2(-3 + 10X2 + -7X4) = 0

Factor a trinomial.
X2((-1 + X2)(3 + -7X2)) = 0

Factor a difference between two squares.
X2(((1 + X)(-1 + X))(3 + -7X2)) = 0

Subproblem 1

Set the factor 'X2' equal to zero and attempt to solve: Simplifying X2 = 0 Solving X2 = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X2 = 0 Take the square root of each side: X = {0}

Subproblem 2

Set the factor '(3 + -7X2)' equal to zero and attempt to solve: Simplifying 3 + -7X2 = 0 Solving 3 + -7X2 = 0 Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7X2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7X2 = 0 + -3 -7X2 = 0 + -3 Combine like terms: 0 + -3 = -3 -7X2 = -3 Divide each side by '-7'. X2 = 0.4285714286 Simplifying X2 = 0.4285714286 Take the square root of each side: X = {-0.654653671, 0.654653671}

Subproblem 3

Set the factor '(1 + X)' equal to zero and attempt to solve: Simplifying 1 + X = 0 Solving 1 + X = 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 + X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + X = 0 + -1 X = 0 + -1 Combine like terms: 0 + -1 = -1 X = -1 Simplifying X = -1

Subproblem 4

Set the factor '(-1 + X)' equal to zero and attempt to solve: Simplifying -1 + X = 0 Solving -1 + X = 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 + X = 0 + 1 Combine like terms: -1 + 1 = 0 0 + X = 0 + 1 X = 0 + 1 Combine like terms: 0 + 1 = 1 X = 1 Simplifying X = 1

Solution

X = {0, -0.654653671, 0.654653671, -1, 1}

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