-10x^4+100x^2+160=0

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Solution for -10x^4+100x^2+160=0 equation:


Simplifying
-10x4 + 100x2 + 160 = 0

Reorder the terms:
160 + 100x2 + -10x4 = 0

Solving
160 + 100x2 + -10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(16 + 10x2 + -1x4) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(16 + 10x2 + -1x4)' equal to zero and attempt to solve: Simplifying 16 + 10x2 + -1x4 = 0 Solving 16 + 10x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + -10x2 + x4 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -10x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + -10x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -10x2 + x4 = 0 + 16 -10x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 -10x2 + x4 = 16 The x term is -10x2. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x2 + 25 + x4 = 16 + 25 Reorder the terms: 25 + -10x2 + x4 = 16 + 25 Combine like terms: 16 + 25 = 41 25 + -10x2 + x4 = 41 Factor a perfect square on the left side: (x2 + -5)(x2 + -5) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x2 + -5) equal to 6.403124237 and -6.403124237.

Subproblem 1

x2 + -5 = 6.403124237 Simplifying x2 + -5 = 6.403124237 Reorder the terms: -5 + x2 = 6.403124237 Solving -5 + x2 = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = 6.403124237 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 6.403124237 + 5 x2 = 6.403124237 + 5 Combine like terms: 6.403124237 + 5 = 11.403124237 x2 = 11.403124237 Simplifying x2 = 11.403124237 Take the square root of each side: x = {-3.376851231, 3.376851231}

Subproblem 2

x2 + -5 = -6.403124237 Simplifying x2 + -5 = -6.403124237 Reorder the terms: -5 + x2 = -6.403124237 Solving -5 + x2 = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = -6.403124237 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -6.403124237 + 5 x2 = -6.403124237 + 5 Combine like terms: -6.403124237 + 5 = -1.403124237 x2 = -1.403124237 Simplifying x2 = -1.403124237 Reorder the terms: 1.403124237 + x2 = -1.403124237 + 1.403124237 Combine like terms: -1.403124237 + 1.403124237 = 0.000000000 1.403124237 + 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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