4m^4-44m^2-40=0

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Solution for 4m^4-44m^2-40=0 equation:


Simplifying
4m4 + -44m2 + -40 = 0

Reorder the terms:
-40 + -44m2 + 4m4 = 0

Solving
-40 + -44m2 + 4m4 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + -11m2 + m4) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-10 + -11m2 + m4)' equal to zero and attempt to solve: Simplifying -10 + -11m2 + m4 = 0 Solving -10 + -11m2 + m4 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -11m2 + 10 + m4 = 0 + 10 Reorder the terms: -10 + 10 + -11m2 + m4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -11m2 + m4 = 0 + 10 -11m2 + m4 = 0 + 10 Combine like terms: 0 + 10 = 10 -11m2 + m4 = 10 The m term is -11m2. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11m2 + 30.25 + m4 = 10 + 30.25 Reorder the terms: 30.25 + -11m2 + m4 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + -11m2 + m4 = 40.25 Factor a perfect square on the left side: (m2 + -5.5)(m2 + -5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (m2 + -5.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

m2 + -5.5 = 6.34428877 Simplifying m2 + -5.5 = 6.34428877 Reorder the terms: -5.5 + m2 = 6.34428877 Solving -5.5 + m2 = 6.34428877 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m2 = 6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m2 = 6.34428877 + 5.5 m2 = 6.34428877 + 5.5 Combine like terms: 6.34428877 + 5.5 = 11.84428877 m2 = 11.84428877 Simplifying m2 = 11.84428877 Take the square root of each side: m = {-3.44155325, 3.44155325}

Subproblem 2

m2 + -5.5 = -6.34428877 Simplifying m2 + -5.5 = -6.34428877 Reorder the terms: -5.5 + m2 = -6.34428877 Solving -5.5 + m2 = -6.34428877 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m2 = -6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m2 = -6.34428877 + 5.5 m2 = -6.34428877 + 5.5 Combine like terms: -6.34428877 + 5.5 = -0.84428877 m2 = -0.84428877 Simplifying m2 = -0.84428877 Reorder the terms: 0.84428877 + m2 = -0.84428877 + 0.84428877 Combine like terms: -0.84428877 + 0.84428877 = 0.00000000 0.84428877 + m2 = 0.00000000 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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