4x^4=9x^2

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Solution for 4x^4=9x^2 equation:


Simplifying
4x4 = 9x2

Solving
4x4 = 9x2

Solving for variable 'x'.

Reorder the terms:
-9x2 + 4x4 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-9x2 + 4x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-9 + 4x2) = 0

Factor a difference between two squares.
x2((3 + 2x)(-3 + 2x)) = 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 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Subproblem 3

Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5

Solution

x = {0, -1.5, 1.5}

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