3x^4+15x^2-24=0

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Solution for 3x^4+15x^2-24=0 equation:


Simplifying
3x4 + 15x2 + -24 = 0

Reorder the terms:
-24 + 15x2 + 3x4 = 0

Solving
-24 + 15x2 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 5x2 + x4) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-8 + 5x2 + x4)' equal to zero and attempt to solve: Simplifying -8 + 5x2 + x4 = 0 Solving -8 + 5x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 5x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + 5x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5x2 + x4 = 0 + 8 5x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 5x2 + x4 = 8 The x term is 5x2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x2 + 6.25 + x4 = 8 + 6.25 Reorder the terms: 6.25 + 5x2 + x4 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + 5x2 + x4 = 14.25 Factor a perfect square on the left side: (x2 + 2.5)(x2 + 2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x2 + 2.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x2 + 2.5 = 3.774917218 Simplifying x2 + 2.5 = 3.774917218 Reorder the terms: 2.5 + x2 = 3.774917218 Solving 2.5 + x2 = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 3.774917218 + -2.5 x2 = 3.774917218 + -2.5 Combine like terms: 3.774917218 + -2.5 = 1.274917218 x2 = 1.274917218 Simplifying x2 = 1.274917218 Take the square root of each side: x = {-1.129122322, 1.129122322}

Subproblem 2

x2 + 2.5 = -3.774917218 Simplifying x2 + 2.5 = -3.774917218 Reorder the terms: 2.5 + x2 = -3.774917218 Solving 2.5 + x2 = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -3.774917218 + -2.5 x2 = -3.774917218 + -2.5 Combine like terms: -3.774917218 + -2.5 = -6.274917218 x2 = -6.274917218 Simplifying x2 = -6.274917218 Reorder the terms: 6.274917218 + x2 = -6.274917218 + 6.274917218 Combine like terms: -6.274917218 + 6.274917218 = 0.000000000 6.274917218 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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