2(x^4+2x^2+1-10x^2-10+20x^2)=0

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Solution for 2(x^4+2x^2+1-10x^2-10+20x^2)=0 equation:


Simplifying
2(x4 + 2x2 + 1 + -10x2 + -10 + 20x2) = 0

Reorder the terms:
2(1 + -10 + 2x2 + -10x2 + 20x2 + x4) = 0

Combine like terms: 1 + -10 = -9
2(-9 + 2x2 + -10x2 + 20x2 + x4) = 0

Combine like terms: 2x2 + -10x2 = -8x2
2(-9 + -8x2 + 20x2 + x4) = 0

Combine like terms: -8x2 + 20x2 = 12x2
2(-9 + 12x2 + x4) = 0
(-9 * 2 + 12x2 * 2 + x4 * 2) = 0
(-18 + 24x2 + 2x4) = 0

Solving
-18 + 24x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 12x2 + x4) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + 12x2 + x4)' equal to zero and attempt to solve: Simplifying -9 + 12x2 + x4 = 0 Solving -9 + 12x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 12x2 + 9 + x4 = 0 + 9 Reorder the terms: -9 + 9 + 12x2 + x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 12x2 + x4 = 0 + 9 12x2 + x4 = 0 + 9 Combine like terms: 0 + 9 = 9 12x2 + x4 = 9 The x term is 12x2. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x2 + 36 + x4 = 9 + 36 Reorder the terms: 36 + 12x2 + x4 = 9 + 36 Combine like terms: 9 + 36 = 45 36 + 12x2 + x4 = 45 Factor a perfect square on the left side: (x2 + 6)(x2 + 6) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x2 + 6) equal to 6.708203933 and -6.708203933.

Subproblem 1

x2 + 6 = 6.708203933 Simplifying x2 + 6 = 6.708203933 Reorder the terms: 6 + x2 = 6.708203933 Solving 6 + x2 = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = 6.708203933 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 6.708203933 + -6 x2 = 6.708203933 + -6 Combine like terms: 6.708203933 + -6 = 0.708203933 x2 = 0.708203933 Simplifying x2 = 0.708203933 Take the square root of each side: x = {-0.841548533, 0.841548533}

Subproblem 2

x2 + 6 = -6.708203933 Simplifying x2 + 6 = -6.708203933 Reorder the terms: 6 + x2 = -6.708203933 Solving 6 + x2 = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = -6.708203933 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -6.708203933 + -6 x2 = -6.708203933 + -6 Combine like terms: -6.708203933 + -6 = -12.708203933 x2 = -12.708203933 Simplifying x2 = -12.708203933 Reorder the terms: 12.708203933 + x2 = -12.708203933 + 12.708203933 Combine like terms: -12.708203933 + 12.708203933 = 0.000000000 12.708203933 + 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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