(7m^4-2m^2)-(5m^4-5m^2+8)=

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Solution for (7m^4-2m^2)-(5m^4-5m^2+8)= equation:


Simplifying
(7m4 + -2m2) + -1(5m4 + -5m2 + 8) = 0

Reorder the terms:
(-2m2 + 7m4) + -1(5m4 + -5m2 + 8) = 0

Remove parenthesis around (-2m2 + 7m4)
-2m2 + 7m4 + -1(5m4 + -5m2 + 8) = 0

Reorder the terms:
-2m2 + 7m4 + -1(8 + -5m2 + 5m4) = 0
-2m2 + 7m4 + (8 * -1 + -5m2 * -1 + 5m4 * -1) = 0
-2m2 + 7m4 + (-8 + 5m2 + -5m4) = 0

Reorder the terms:
-8 + -2m2 + 5m2 + 7m4 + -5m4 = 0

Combine like terms: -2m2 + 5m2 = 3m2
-8 + 3m2 + 7m4 + -5m4 = 0

Combine like terms: 7m4 + -5m4 = 2m4
-8 + 3m2 + 2m4 = 0

Solving
-8 + 3m2 + 2m4 = 0

Solving for variable 'm'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-4 + 1.5m2 + m4 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.5m2 + 4 + m4 = 0 + 4

Reorder the terms:
-4 + 4 + 1.5m2 + m4 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.5m2 + m4 = 0 + 4
1.5m2 + m4 = 0 + 4

Combine like terms: 0 + 4 = 4
1.5m2 + m4 = 4

The m term is 1.5m2.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5m2 + 0.5625 + m4 = 4 + 0.5625

Reorder the terms:
0.5625 + 1.5m2 + m4 = 4 + 0.5625

Combine like terms: 4 + 0.5625 = 4.5625
0.5625 + 1.5m2 + m4 = 4.5625

Factor a perfect square on the left side:
(m2 + 0.75)(m2 + 0.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(m2 + 0.75) equal to 2.136000936 and -2.136000936.

Subproblem 1

m2 + 0.75 = 2.136000936 Simplifying m2 + 0.75 = 2.136000936 Reorder the terms: 0.75 + m2 = 2.136000936 Solving 0.75 + m2 = 2.136000936 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m2 = 2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m2 = 2.136000936 + -0.75 m2 = 2.136000936 + -0.75 Combine like terms: 2.136000936 + -0.75 = 1.386000936 m2 = 1.386000936 Simplifying m2 = 1.386000936 Take the square root of each side: m = {-1.17728541, 1.17728541}

Subproblem 2

m2 + 0.75 = -2.136000936 Simplifying m2 + 0.75 = -2.136000936 Reorder the terms: 0.75 + m2 = -2.136000936 Solving 0.75 + m2 = -2.136000936 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m2 = -2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m2 = -2.136000936 + -0.75 m2 = -2.136000936 + -0.75 Combine like terms: -2.136000936 + -0.75 = -2.886000936 m2 = -2.886000936 Simplifying m2 = -2.886000936 Reorder the terms: 2.886000936 + m2 = -2.886000936 + 2.886000936 Combine like terms: -2.886000936 + 2.886000936 = 0.000000000 2.886000936 + m2 = 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.

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