m^2(m^2-4)=3m^2-8

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Solution for m^2(m^2-4)=3m^2-8 equation:


Simplifying
m2(m2 + -4) = 3m2 + -8

Reorder the terms:
m2(-4 + m2) = 3m2 + -8
(-4 * m2 + m2 * m2) = 3m2 + -8
(-4m2 + m4) = 3m2 + -8

Reorder the terms:
-4m2 + m4 = -8 + 3m2

Solving
-4m2 + m4 = -8 + 3m2

Solving for variable 'm'.

Reorder the terms:
8 + -4m2 + -3m2 + m4 = -8 + 3m2 + 8 + -3m2

Combine like terms: -4m2 + -3m2 = -7m2
8 + -7m2 + m4 = -8 + 3m2 + 8 + -3m2

Reorder the terms:
8 + -7m2 + m4 = -8 + 8 + 3m2 + -3m2

Combine like terms: -8 + 8 = 0
8 + -7m2 + m4 = 0 + 3m2 + -3m2
8 + -7m2 + m4 = 3m2 + -3m2

Combine like terms: 3m2 + -3m2 = 0
8 + -7m2 + m4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7m2 + -8 + m4 = 0 + -8

Reorder the terms:
8 + -8 + -7m2 + m4 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7m2 + m4 = 0 + -8
-7m2 + m4 = 0 + -8

Combine like terms: 0 + -8 = -8
-7m2 + m4 = -8

The m term is -7m2.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7m2 + 12.25 + m4 = -8 + 12.25

Reorder the terms:
12.25 + -7m2 + m4 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7m2 + m4 = 4.25

Factor a perfect square on the left side:
(m2 + -3.5)(m2 + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(m2 + -3.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

m2 + -3.5 = 2.061552813 Simplifying m2 + -3.5 = 2.061552813 Reorder the terms: -3.5 + m2 = 2.061552813 Solving -3.5 + m2 = 2.061552813 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m2 = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m2 = 2.061552813 + 3.5 m2 = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 m2 = 5.561552813 Simplifying m2 = 5.561552813 Take the square root of each side: m = {-2.358294471, 2.358294471}

Subproblem 2

m2 + -3.5 = -2.061552813 Simplifying m2 + -3.5 = -2.061552813 Reorder the terms: -3.5 + m2 = -2.061552813 Solving -3.5 + m2 = -2.061552813 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m2 = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m2 = -2.061552813 + 3.5 m2 = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 m2 = 1.438447187 Simplifying m2 = 1.438447187 Take the square root of each side: m = {-1.19935282, 1.19935282}

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-2.358294471, 2.358294471, -1.19935282, 1.19935282}

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